-6x + 2y = -32 4x + 3y = -9

Answer 1

To solve this system of linear equations, we can use either the substitution method or the elimination method.

Let's use the elimination method to solve this system of equations.

1. Multiply the first equation by 2 to make the coefficients of y equal:

-12x + 4y = -64

2. Rewrite the second equation:

4x + 3y = -9

3. Add the two equations together to eliminate y:

(-12x + 4y) + (4x + 3y) = -64 - 9
-8x + 7y = -73

4. Now, we have a new equation in terms of x and y. Let's solve for x:

-8x = -73 - 7y
x = (-73 - 7y) / -8

5. Substitute the expression for x into one of the original equations. Let's use the first equation:

-6((-73 - 7y) / 8) + 2y = -32
(438 + 42y) / 8 + 2y = -32
(438 + 42y + 16y) / 8 = -32
(438 + 58y) / 8 = -32
438 + 58y = -256
58y = -694
y = -694 / 58
y = -12

6. Substitute the value of y back into the expression for x:

x = (-73 - 7(-12)) / -8
x = (-73 + 84) / -8
x = 11 / -8
x = -1.375

Therefore, the solution to the system of equations is x = -1.375 and y = -12.