Question

Solve the system using elimination.

5x + 8y = –29
7x – 2y = –67





(–1, –3)


(–9, 2)


(–7, 9)

Answer 1

To solve the system using elimination, we need to eliminate one variable by manipulating the equations.

First, let's multiply the first equation by 2 and the second equation by 8 to make the coefficients of y the same:


2(5x + 8y) = 2(-29)
8(7x - 2y) = 8(-67)


Simplifying, we get:


10x + 16y = -58
56x - 16y = -536


Now we can add the two equations:


(10x + 16y) + (56x - 16y) = -58 + (-536)


Simplifying, we get:


66x = -594


Dividing both sides by 66:


x = -9


Now we can substitute this value of x back into one of the original equations. Let's use the first equation:


5x + 8y = -29


5(-9) + 8y = -29


-45 + 8y = -29


Adding 45 to both sides:


8y = 16


Dividing both sides by 8:


y = 2


Therefore, the solution to the system of equations is (-9, 2).