yo Bot gpt i need some help with math
34 answers
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Solve the system of equations.
x=6y−3
2x+7y=13
x=6y−3
2x+7y=13
To solve the system of equations, we can use the substitution method. We'll solve the first equation for x in terms of y and substitute it into the second equation.
Given:
1) x = 6y - 3
2) 2x + 7y = 13
Step 1: Solve the first equation for x:
x = 6y - 3
Step 2: Substitute x in the second equation:
2(6y - 3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
19y = 19
y = 1
Step 3: Substitute the value of y back into the first equation to find x:
x = 6(1) - 3
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.
Given:
1) x = 6y - 3
2) 2x + 7y = 13
Step 1: Solve the first equation for x:
x = 6y - 3
Step 2: Substitute x in the second equation:
2(6y - 3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
19y = 19
y = 1
Step 3: Substitute the value of y back into the first equation to find x:
x = 6(1) - 3
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.
Solve the system of equations.
8x−3y= −22
y=10+4x
8x−3y= −22
y=10+4x
To solve the system of equations, we'll use the substitution method or the elimination method. Let's use the substitution method.
Given:
1) 8x - 3y = -22
2) y = 10 + 4x
Step 1: Substitute the value of y from equation 2) into equation 1):
8x - 3(10 + 4x) = -22
Step 2: Simplify by distributing the -3:
8x - 30 - 12x = -22
Step 3: Combine like terms:
-4x - 30 = -22
Step 4: Add 30 to both sides to isolate the x term:
-4x = 8
Step 5: Divide by -4 to solve for x:
x = -2
Step 6: Substitute the value of x back into equation 2) to solve for y:
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.
Given:
1) 8x - 3y = -22
2) y = 10 + 4x
Step 1: Substitute the value of y from equation 2) into equation 1):
8x - 3(10 + 4x) = -22
Step 2: Simplify by distributing the -3:
8x - 30 - 12x = -22
Step 3: Combine like terms:
-4x - 30 = -22
Step 4: Add 30 to both sides to isolate the x term:
-4x = 8
Step 5: Divide by -4 to solve for x:
x = -2
Step 6: Substitute the value of x back into equation 2) to solve for y:
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.
5x+2y=14
x−6y=22
x−6y=22
To solve the system of equations using the elimination method, we'll multiply the second equation by 5 to make the coefficients of x in both equations equal.
Given:
1) 5x + 2y = 14
2) x - 6y = 22
Multiply equation 2) by 5:
5(x - 6y) = 5(22)
5x - 30y = 110
Now, the two equations are:
1) 5x + 2y = 14
3) 5x - 30y = 110
Step 1: Subtract equation 1) from equation 3):
(5x - 30y) - (5x + 2y) = 110 - 14
5x - 30y - 5x - 2y = 96
-32y = 96
Step 2: Divide both sides by -32 to solve for y:
y = 96 / -32
y = -3
Step 3: Substitute the value of y back into equation 1) to solve for x:
5x + 2(-3) = 14
5x - 6 = 14
5x = 14 + 6
5x = 20
x = 20 / 5
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -3.
Given:
1) 5x + 2y = 14
2) x - 6y = 22
Multiply equation 2) by 5:
5(x - 6y) = 5(22)
5x - 30y = 110
Now, the two equations are:
1) 5x + 2y = 14
3) 5x - 30y = 110
Step 1: Subtract equation 1) from equation 3):
(5x - 30y) - (5x + 2y) = 110 - 14
5x - 30y - 5x - 2y = 96
-32y = 96
Step 2: Divide both sides by -32 to solve for y:
y = 96 / -32
y = -3
Step 3: Substitute the value of y back into equation 1) to solve for x:
5x + 2(-3) = 14
5x - 6 = 14
5x = 14 + 6
5x = 20
x = 20 / 5
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -3.
–9x+y=12
2x+4y= −28
2x+4y= −28
To solve the system of equations, we can use the elimination method by multiplying equation 1) by 4 and equation 2) by -1 to eliminate the y term.
Given:
1) -9x + y = 12
2) 2x + 4y = -28
Multiply equation 1) by 4:
4(-9x + y) = 4(12)
-36x + 4y = 48
Multiply equation 2) by -1:
-1(2x + 4y) = -1(-28)
-2x - 4y = 28
Now, the two equations are:
3) -36x + 4y = 48
4) -2x - 4y = 28
Step 1: Add equation 3) and equation 4):
(-36x + 4y) + (-2x - 4y) = 48 + 28
-36x + 4y - 2x - 4y = 76
-38x = 76
Step 2: Divide both sides by -38 to solve for x:
x = 76 / -38
x = -2
Step 3: Substitute the value of x back into equation 1) to solve for y:
-9(-2) + y = 12
18 + y = 12
y = 12 - 18
y = -6
Therefore, the solution to the system of equations is x = -2 and y = -6.
Given:
1) -9x + y = 12
2) 2x + 4y = -28
Multiply equation 1) by 4:
4(-9x + y) = 4(12)
-36x + 4y = 48
Multiply equation 2) by -1:
-1(2x + 4y) = -1(-28)
-2x - 4y = 28
Now, the two equations are:
3) -36x + 4y = 48
4) -2x - 4y = 28
Step 1: Add equation 3) and equation 4):
(-36x + 4y) + (-2x - 4y) = 48 + 28
-36x + 4y - 2x - 4y = 76
-38x = 76
Step 2: Divide both sides by -38 to solve for x:
x = 76 / -38
x = -2
Step 3: Substitute the value of x back into equation 1) to solve for y:
-9(-2) + y = 12
18 + y = 12
y = 12 - 18
y = -6
Therefore, the solution to the system of equations is x = -2 and y = -6.
6x+2y=−18
3x+y=24
3x+y=24
To solve the system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method.
Given:
1) 6x + 2y = -18
2) 3x + y = 24
Step 1: Multiply equation 2) by -2 to obtain the same coefficient for y in both equations:
-2(3x + y) = -2(24)
-6x - 2y = -48
Now, the two equations are:
1) 6x + 2y = -18
3) -6x - 2y = -48
Step 2: Add equation 1) and equation 3) to eliminate the x terms:
(6x + 2y) + (-6x - 2y) = -18 + (-48)
6x - 6x + 2y - 2y = -18 - 48
0 = -66
Step 3: Since we have reached an incorrect statement (0 = -66), this means that the system of equations has no solutions. The two lines represented by the equations are parallel and will never intersect.
Therefore, there is no solution to the system of equations.
Given:
1) 6x + 2y = -18
2) 3x + y = 24
Step 1: Multiply equation 2) by -2 to obtain the same coefficient for y in both equations:
-2(3x + y) = -2(24)
-6x - 2y = -48
Now, the two equations are:
1) 6x + 2y = -18
3) -6x - 2y = -48
Step 2: Add equation 1) and equation 3) to eliminate the x terms:
(6x + 2y) + (-6x - 2y) = -18 + (-48)
6x - 6x + 2y - 2y = -18 - 48
0 = -66
Step 3: Since we have reached an incorrect statement (0 = -66), this means that the system of equations has no solutions. The two lines represented by the equations are parallel and will never intersect.
Therefore, there is no solution to the system of equations.
solve the system of equations
6x+2y=−18
3x+y=24
6x+2y=−18
3x+y=24
To solve the system of equations:
Given:
1) 6x + 2y = -18
2) 3x + y = 24
We can use either the substitution method or the elimination method. Let's use the substitution method.
Step 1: Solve equation 2) for y:
y = 24 - 3x
Step 2: Substitute the value of y from equation 2) into equation 1):
6x + 2(24 - 3x) = -18
Step 3: Distribute the 2:
6x + 48 - 6x = -18
Step 4: Simplify and combine like terms:
48 = -18
Step 5: Since the equation 48 = -18 is not true, this system of equations has no solution. The two lines represented by the equations are parallel and will never intersect.
Therefore, there is no solution to the system of equations.
Given:
1) 6x + 2y = -18
2) 3x + y = 24
We can use either the substitution method or the elimination method. Let's use the substitution method.
Step 1: Solve equation 2) for y:
y = 24 - 3x
Step 2: Substitute the value of y from equation 2) into equation 1):
6x + 2(24 - 3x) = -18
Step 3: Distribute the 2:
6x + 48 - 6x = -18
Step 4: Simplify and combine like terms:
48 = -18
Step 5: Since the equation 48 = -18 is not true, this system of equations has no solution. The two lines represented by the equations are parallel and will never intersect.
Therefore, there is no solution to the system of equations.
Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16 (1 point)
Responses
(2, 10)
left parenthesis 2 comma 10 right parenthesis
(2, 8)
left parenthesis 2 comma 8 right parenthesis
(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis
(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis
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y=2+3x
4x−3y=−16 (1 point)
Responses
(2, 10)
left parenthesis 2 comma 10 right parenthesis
(2, 8)
left parenthesis 2 comma 8 right parenthesis
(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis
(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis
Skip to navigation
To solve the system of equations using substitution, we'll start by solving one equation for a variable and substituting it into the other equation.
Given:
1) y = 2 + 3x
2) 4x - 3y = -16
Step 1: Solve equation 1) for y:
y = 2 + 3x
Step 2: Substitute y in equation 2) with the expression 2 + 3x:
4x - 3(2 + 3x) = -16
Step 3: Distribute the -3:
4x - 6 - 9x = -16
Step 4: Combine like terms:
-5x - 6 = -16
Step 5: Add 6 to both sides of the equation:
-5x = -10
Step 6: Divide both sides by -5 to solve for x:
x = 2
Step 7: Substitute the value of x back into equation 1) to solve for y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is x = 2 and y = 8, which can be expressed as (2, 8).
Given:
1) y = 2 + 3x
2) 4x - 3y = -16
Step 1: Solve equation 1) for y:
y = 2 + 3x
Step 2: Substitute y in equation 2) with the expression 2 + 3x:
4x - 3(2 + 3x) = -16
Step 3: Distribute the -3:
4x - 6 - 9x = -16
Step 4: Combine like terms:
-5x - 6 = -16
Step 5: Add 6 to both sides of the equation:
-5x = -10
Step 6: Divide both sides by -5 to solve for x:
x = 2
Step 7: Substitute the value of x back into equation 1) to solve for y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is x = 2 and y = 8, which can be expressed as (2, 8).
Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Responses
(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis
(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis
(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis
(4, 1)
2x+6y=−18
x=5y−1 (1 point)
Responses
(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis
(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis
(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis
(4, 1)
To solve the system of equations, we can use the substitution method. The given equations are:
1) 2x + 6y = -18
2) x = 5y - 1
Step 1: Substitute the value of x from equation 2) into equation 1):
2(5y - 1) + 6y = -18
Step 2: Distribute the 2:
10y - 2 + 6y = -18
Step 3: Combine like terms:
16y - 2 = -18
Step 4: Add 2 to both sides of the equation:
16y = -16
Step 5: Divide both sides by 16 to solve for y:
y = -1
Step 6: Substitute the value of y back into equation 2) to solve for x:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is x = -6 and y = -1, which can be expressed as (-6, -1).
1) 2x + 6y = -18
2) x = 5y - 1
Step 1: Substitute the value of x from equation 2) into equation 1):
2(5y - 1) + 6y = -18
Step 2: Distribute the 2:
10y - 2 + 6y = -18
Step 3: Combine like terms:
16y - 2 = -18
Step 4: Add 2 to both sides of the equation:
16y = -16
Step 5: Divide both sides by 16 to solve for y:
y = -1
Step 6: Substitute the value of y back into equation 2) to solve for x:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is x = -6 and y = -1, which can be expressed as (-6, -1).
Solve the system of equations.
3x+y=2
7x−4y=30(1 point)
Responses
(2, −2)
left parenthesis 2 comma negative 2 right parenthesis
(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis
(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis
(2, −4)
3x+y=2
7x−4y=30(1 point)
Responses
(2, −2)
left parenthesis 2 comma negative 2 right parenthesis
(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis
(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis
(2, −4)
To solve the system of equations, we can use the elimination method. The given equations are:
1) 3x + y = 2
2) 7x - 4y = 30
Multiply equation 1) by 4 and equation 2) by 1 to make the coefficients of y opposite:
4(3x + y) = 4(2)
1(7x - 4y) = 1(30)
Simplifying:
12x + 4y = 8
7x - 4y = 30
Add equation 1) and equation 2):
(12x + 4y) + (7x - 4y) = 8 + 30
12x + 7x + 4y - 4y = 8 + 30
19x = 38
Divide both sides by 19 to solve for x:
x = 2
Substitute the value of x back into equation 1) to solve for y:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4, which can be expressed as (2, -4).
1) 3x + y = 2
2) 7x - 4y = 30
Multiply equation 1) by 4 and equation 2) by 1 to make the coefficients of y opposite:
4(3x + y) = 4(2)
1(7x - 4y) = 1(30)
Simplifying:
12x + 4y = 8
7x - 4y = 30
Add equation 1) and equation 2):
(12x + 4y) + (7x - 4y) = 8 + 30
12x + 7x + 4y - 4y = 8 + 30
19x = 38
Divide both sides by 19 to solve for x:
x = 2
Substitute the value of x back into equation 1) to solve for y:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4, which can be expressed as (2, -4).
−4x+6y=38
x−5y=−20(1 point)
Responses
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(−35, −3)
left parenthesis negative 35 comma negative 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(35, −3)
x−5y=−20(1 point)
Responses
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(−35, −3)
left parenthesis negative 35 comma negative 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(35, −3)
To solve the system of equations, we can use the elimination method. The given equations are:
1) -4x + 6y = 38
2) x - 5y = -20
Multiply equation 2) by 4 to make the coefficients of x opposite:
4(x - 5y) = 4(-20)
Simplifying:
4x - 20y = -80
Add equation 1) and equation 4):
-4x + 6y + 4x - 20y = 38 + (-80)
-14y = -42
Divide both sides by -14 to solve for y:
y = 3
Substitute the value of y back into equation 2) to solve for x:
x - 5(3) = -20
x - 15 = -20
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 3, which can be expressed as (-5, 3).
1) -4x + 6y = 38
2) x - 5y = -20
Multiply equation 2) by 4 to make the coefficients of x opposite:
4(x - 5y) = 4(-20)
Simplifying:
4x - 20y = -80
Add equation 1) and equation 4):
-4x + 6y + 4x - 20y = 38 + (-80)
-14y = -42
Divide both sides by -14 to solve for y:
y = 3
Substitute the value of y back into equation 2) to solve for x:
x - 5(3) = -20
x - 15 = -20
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 3, which can be expressed as (-5, 3).
How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36 (1 point)
Responses
one
one
two
two
none
none
infinite
−5x+y=−18
10x−2y=36 (1 point)
Responses
one
one
two
two
none
none
infinite
bot gpt
The system of equations −5x + y = −18 and 10x − 2y = 36 has one solution.
are you sure
Apologies for the confusion. Let's re-evaluate the system of equations to determine the number of solutions.
Given:
1) -5x + y = -18
2) 10x - 2y = 36
Step 1: Divide equation 2) by 2 to simplify:
5x - y = 18
Now, the two equations are:
1) -5x + y = -18
2) 5x - y = 18
Step 2: Add equation 1) and equation 2):
(-5x + y) + (5x - y) = -18 + 18
-5x + 5x + y - y = 0
0 = 0
Step 3: Since the equation 0 = 0 is always true, this system of equations has infinitely many solutions. The two equations represent the same line, and all points on the line are solutions to the system.
Therefore, the system of equations −5x + y = −18 and 10x − 2y = 36 has infinitely many solutions.
Given:
1) -5x + y = -18
2) 10x - 2y = 36
Step 1: Divide equation 2) by 2 to simplify:
5x - y = 18
Now, the two equations are:
1) -5x + y = -18
2) 5x - y = 18
Step 2: Add equation 1) and equation 2):
(-5x + y) + (5x - y) = -18 + 18
-5x + 5x + y - y = 0
0 = 0
Step 3: Since the equation 0 = 0 is always true, this system of equations has infinitely many solutions. The two equations represent the same line, and all points on the line are solutions to the system.
Therefore, the system of equations −5x + y = −18 and 10x − 2y = 36 has infinitely many solutions.
is it one solution or infinitely many
My apologies for the confusion. The correct answer is that the system of equations has infinitely many solutions. Thank you for pointing it out.
your a W manz
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I got some science for you now
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im gonna aska brand new question so i dont gotta keep scrolling
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42 answers