Solve the system using elimination.
-10x - 3y = -18
-7x - 8y = 11
To solve this system using elimination, we need to multiply one or both of the equations by a constant so that we can eliminate one of the variables when we add the two equations together.
First, let's multiply the first equation by 8 and the second equation by 3 to make the coefficients of y the same when we add them together:
-10(8x) - 3(8y) = -18(8)
-7(3x) - 8(3y) = 11(3)
This simplifies to:
-80x - 24y = -144
-21x - 24y = 33
Now, let's add the two equations together:
-80x - 24y + (-21x - 24y) = -144 + 33
-101x - 48y = -111
Now, we have one equation with one variable to solve:
-101x - 48y = -111
We can solve for x by isolating x:
-101x = -111 + 48y
x = (111 - 48y) / 101
Now, we can substitute this expression for x back into either of the original equations to solve for y. Let's use the first equation:
-10((111 - 48y) / 101) - 3y = -18
Multiplying by 101 to clear denominators and simplify:
-10(111 - 48y) - 303y = -1818
-1110 + 480y - 303y = -1818
177y = 292
y = 292 / 177
y ≈ 1.65
Now that we have found the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the second equation:
-7x - 8(1.65) = 11
-7x - 13.2 = 11
-7x = 24.2
x = 24.2 / -7
x ≈ -3.46
Therefore, the solution to the system of equations is x ≈ -3.46 and y ≈ 1.65.