Solve the system of equations. -6x+2y=-32. 4x+3y=-9
To solve the system of equations using elimination, we multiply the first equation by 3 and the second equation by 2 to create a system where the coefficients of y will cancel each other out:
3(-6x + 2y) = 3(-32)
2(4x + 3y) = 2(-9)
Simplifying these equations gives us:
-18x + 6y = -96
8x + 6y = -18
Adding the two equations together eliminates the y variable:
(-18x + 6y) + (8x + 6y) = -96 + (-18)
-10x = -114
Dividing both sides of the equation by -10 gives:
x = -114/-10
x = 11.4
Substituting the value of x into the second equation gives:
4(11.4) + 3y = -9
45.6 + 3y = -9
3y = -9 - 45.6
3y = -54.6
y = -54.6/3
y = -18.2
Therefore, the solution to the system of equations is x = 11.4 and y = -18.2.