-9x + y = 12
2x + 4 y = -28
To solve this system of equations, we can use the method of substitution or elimination.
Let's go with the method of substitution.
From the first equation, rearrange it to solve for y:
-9x + y = 12
y = 9x + 12
Now substitute this expression for y in the second equation:
2x + 4(9x + 12) = -28
2x + 36x + 48 = -28
38x = -76
x = -2
Substitute the value of x in the first equation to find y:
-9(-2) + y = 12
18 + y = 12
y = 12 - 18
y = -6
So the solution to the system of equations is x = -2 and y = -6.
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one variable by adding or subtracting the equations.
1. Multiply the first equation by 2 to make the coefficients of x in both equations the same:
-18x + 2y = 24
2. Multiply the second equation by -9 to make the coefficients of x in both equations the same:
-18x - 36y = 252
3. Now, subtract the second equation from the first equation to eliminate the x term:
(-18x + 2y) - (-18x - 36y) = 24 - 252
-18x + 2y + 18x + 36y = -228
38y = -228
4. Divide both sides of the equation by 38 to solve for y:
y = -228 / 38
y = -6
5. Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
-9x + (-6) = 12
-9x - 6 = 12
-9x = 12 + 6
-9x = 18
6. Divide both sides of the equation by -9 to solve for x:
x = 18 / -9
x = -2
Therefore, the solution to the system of equations is x = -2, y = -6.