Question

What is the solution to the system of equations? 5x-2y=-16 4x-5y=-23

Answer 1

The solution set is {-2, 3}.

Explanation:

We can do this by elimination after manipulating the 2 equations so that the coefficients of y will disappear after addition:

5x - 2y = -16 Multiply this by -5:

-25x + 10y = 80 ...........(A)

4x - 5y = -23 Multiply this by 2:

8x - 10y = -46..............(B)

Now add A and B:

-17x = 34

x = 34/-17

x = -2.

Now substitute x = -2 into the first original equation:

5(-2) - 2y = -16

-2y = -16 +10 = -6

y = -6/-2

y = 3.

Confirm these results by substitution in the second original equation:

4(-2) - 5(3)

= - 8 - 15 = -23.

Checks OK.