1. (3, 1)
2. (4, -6)
3. (-8, -3)
4. (-2, -9)
5. The system of equations has one solution.
1. Solve the system of equations.
x = 6y − 3
2x + 7y = 13
(3, ____)
2. Solve the system of equations.
8x − 3y = −22
y = 10 + 4x
(____, ____)
3. Solve the system of equations.
5x + 2y = 14
x − 6y = 22
(____, -3)
4. Solve the system of equations.
–9x + y = 12
2x + 4y = −28
(-2, ____)
5. How many solutions does the system of equations have?
6x + 2y = −18
3x + y = 24
____.
11 answers
question 1 is correct
Thank you for pointing that out. Here are the correct answers for the remaining questions:
2. (6, -14)
3. (-16, -3)
4. (-2, -17)
5. The system of equations has one solution.
2. (6, -14)
3. (-16, -3)
4. (-2, -17)
5. The system of equations has one solution.
Solve the system of equations.
8x−3y= −22
y=10+4x (1 point)
(
,
)
8x−3y= −22
y=10+4x (1 point)
(
,
)
To solve this system of equations:
8x - 3y = -22
y = 10 + 4x
We can substitute the second equation into the first equation:
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
-4x - 30 = -22
-4x = 8
x = -2
Now that we have x, we can find y by substituting the value of x back into the second equation:
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is (-2, 2).
8x - 3y = -22
y = 10 + 4x
We can substitute the second equation into the first equation:
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
-4x - 30 = -22
-4x = 8
x = -2
Now that we have x, we can find y by substituting the value of x back into the second equation:
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is (-2, 2).
Solve the system of equations.
5x+2y=14
x−6y=22 (1 point)
(
,
)
5x+2y=14
x−6y=22 (1 point)
(
,
)
To solve the system of equations:
5x + 2y = 14
x - 6y = 22
We can use the substitution method to solve this system of equations. Let's solve it:
From the second equation:
x = 6y + 22
Substitute x = 6y + 22 into the first equation:
5(6y + 22) + 2y = 14
30y + 110 + 2y = 14
32y + 110 = 14
32y = -96
y = -3
Now, substitute y = -3 back into x = 6y + 22:
x = 6(-3) + 22
x = -18 + 22
x = 4
Therefore, the solution to the system of equations is (4, -3).
5x + 2y = 14
x - 6y = 22
We can use the substitution method to solve this system of equations. Let's solve it:
From the second equation:
x = 6y + 22
Substitute x = 6y + 22 into the first equation:
5(6y + 22) + 2y = 14
30y + 110 + 2y = 14
32y + 110 = 14
32y = -96
y = -3
Now, substitute y = -3 back into x = 6y + 22:
x = 6(-3) + 22
x = -18 + 22
x = 4
Therefore, the solution to the system of equations is (4, -3).
Solve the system of equations.
–9x+y=12
2x+4y= −28 (1 point)
(
,
)
–9x+y=12
2x+4y= −28 (1 point)
(
,
)
To solve the system of equations:
-9x + y = 12
2x + 4y = -28
We can solve this system of equations using the elimination method. Let's start by multiplying the first equation by 4 and the second equation by 1 to make the coefficients of y equal in magnitude but opposite in sign:
-36x + 4y = 48 (Multiplying the first equation by 4)
2x + 4y = -28 (Second equation remains the same)
Now, adding the two equations to eliminate y:
(-36x + 4y) + (2x + 4y) = 48 - 28
-34x = 20
x = -20/34
x = -10/17
Now, substitute the value of x back into the first equation to solve for y:
-9(-10/17) + y = 12
90/17 + y = 12
y = 12 - 90/17
y = (204 - 90) / 17
y = 114 / 17
y = 6.71 (rounded to 2 decimal places)
Therefore, the solution to the system of equations is (-10/17, 6.71).
-9x + y = 12
2x + 4y = -28
We can solve this system of equations using the elimination method. Let's start by multiplying the first equation by 4 and the second equation by 1 to make the coefficients of y equal in magnitude but opposite in sign:
-36x + 4y = 48 (Multiplying the first equation by 4)
2x + 4y = -28 (Second equation remains the same)
Now, adding the two equations to eliminate y:
(-36x + 4y) + (2x + 4y) = 48 - 28
-34x = 20
x = -20/34
x = -10/17
Now, substitute the value of x back into the first equation to solve for y:
-9(-10/17) + y = 12
90/17 + y = 12
y = 12 - 90/17
y = (204 - 90) / 17
y = 114 / 17
y = 6.71 (rounded to 2 decimal places)
Therefore, the solution to the system of equations is (-10/17, 6.71).
Solve the system of equations.
–9x + y = 12
2x + 4y = −28
(-2, ____)
–9x + y = 12
2x + 4y = −28
(-2, ____)
To solve the system of equations:
-9x + y = 12
2x + 4y = -28
We can solve this system of equations by first solving for x using the first equation and then finding y by substituting the x-value into the second equation.
From the first equation:
y = 9x + 12
Now substitute y = 9x + 12 into the second equation:
2x + 4(9x + 12) = -28
2x + 36x + 48 = -28
38x + 48 = -28
38x = -76
x = -76/38
x = -2
Now substituting x = -2 back into y = 9x + 12:
y = 9(-2) + 12
y = -18 + 12
y = -6
Therefore, the solution to the system of equations is (-2, -6).
-9x + y = 12
2x + 4y = -28
We can solve this system of equations by first solving for x using the first equation and then finding y by substituting the x-value into the second equation.
From the first equation:
y = 9x + 12
Now substitute y = 9x + 12 into the second equation:
2x + 4(9x + 12) = -28
2x + 36x + 48 = -28
38x + 48 = -28
38x = -76
x = -76/38
x = -2
Now substituting x = -2 back into y = 9x + 12:
y = 9(-2) + 12
y = -18 + 12
y = -6
Therefore, the solution to the system of equations is (-2, -6).