To solve the system of equations:
-9x + y = 12 (equation 1)
2x + 4y = -28 (equation 2)
First, let's solve equation 1 for y:
y = 12 + 9x
Next, substitute the value of y from equation 1 into equation 2:
2x + 4(12 + 9x) = -28
2x + 48 + 36x = -28
38x + 48 = -28
38x = -28 - 48
38x = -76
x = -76/38
x = -2
Now that we have found the value of x, we can substitute it back into equation 1 to find the value of y:
y = 12 + 9(-2)
y = 12 - 18
y = -6
Therefore, the solution to the system of equations is x = -2 and y = -6.
solve the system of equations.
-9x + y = 12
2x + 4y = -28
(_,_)
show your work
11 answers
solve the system of two equations using substitution.
y = 2 + 3x
4x - 3y = -16
(_,_)
y = 2 + 3x
4x - 3y = -16
(_,_)
To solve the system of equations by substitution:
1. Substitute the expression for y from the first equation into the second equation:
4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
2. Combine like terms:
4x - 9x - 6 = -16
-5x - 6 = -16
3. Add 6 to both sides of the equation:
-5x = -10
4. Divide by -5 to solve for x:
x = -10 / -5
x = 2
5. Substitute the value of x back into the first equation 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.
1. Substitute the expression for y from the first equation into the second equation:
4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
2. Combine like terms:
4x - 9x - 6 = -16
-5x - 6 = -16
3. Add 6 to both sides of the equation:
-5x = -10
4. Divide by -5 to solve for x:
x = -10 / -5
x = 2
5. Substitute the value of x back into the first equation 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.
solve the system of equations.
2x + 6y = -18
x = 5y - 1
(_,_)
2x + 6y = -18
x = 5y - 1
(_,_)
To solve the system of equations:
1. Substitute the expression for x from the second equation into the first equation:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
2. Substitute the value of y back into the second equation 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.
1. Substitute the expression for x from the second equation into the first equation:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
2. Substitute the value of y back into the second equation 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.
solve the system of equations.
3x + y = 2
7x - 4y = 30
(_,_)
3x + y = 2
7x - 4y = 30
(_,_)
To solve the system of equations:
From the first equation:
y = 2 - 3x (equation 1)
Substitute this expression for y into the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38 / 19
x = 2
Substitute the value of x back into equation 1 to solve for y:
y = 2 - 3(2)
y = 2 - 6
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4.
From the first equation:
y = 2 - 3x (equation 1)
Substitute this expression for y into the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38 / 19
x = 2
Substitute the value of x back into equation 1 to solve for y:
y = 2 - 3(2)
y = 2 - 6
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4.
solve the system of equations.
-4x + 6y = 38
x - 5y = -20
(_,_)
-4x + 6y = 38
x - 5y = -20
(_,_)
To solve the system of equations:
First, multiply the second equation by 4 to eliminate x:
4(x - 5y) = 4(-20)
4x - 20y = -80
Now, we have the system of equations:
-4x + 6y = 38
4x - 20y = -80
Adding the two equations together to eliminate x:
-14y = -42
y = 3
Substitute y = 3 back into the second equation to find x:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 3.
First, multiply the second equation by 4 to eliminate x:
4(x - 5y) = 4(-20)
4x - 20y = -80
Now, we have the system of equations:
-4x + 6y = 38
4x - 20y = -80
Adding the two equations together to eliminate x:
-14y = -42
y = 3
Substitute y = 3 back into the second equation to find x:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 3.
how many solution(s) does the system of equations have?
-5x + y = -18
10x - 2y = 36
-5x + y = -18
10x - 2y = 36
To determine the number of solutions for the system of equations:
-5x + y = -18
10x - 2y = 36
We can simplify the second equation by dividing by 2:
5x - y = 18
Now we can compare the two equations:
-5x + y = -18
5x - y = 18
Adding the two equations together:
0 = 0
This equation tells us that the two original equations are equivalent and represent the same line. The two equations have infinitely many solutions since the two lines coincide and overlap completely.
-5x + y = -18
10x - 2y = 36
We can simplify the second equation by dividing by 2:
5x - y = 18
Now we can compare the two equations:
-5x + y = -18
5x - y = 18
Adding the two equations together:
0 = 0
This equation tells us that the two original equations are equivalent and represent the same line. The two equations have infinitely many solutions since the two lines coincide and overlap completely.