Question

What is the solution of the system? 5x + 2y = 9 4x - 3y = 44

Answer 1

Hello!

`\large\boxed{5, -8}`

5x + 2y = 9

4x - 3y = 44

We can eliminate y by multiplying both expressions in order to have the y coefficients equal.

The LCM (least common multiple) of 2 and 3 is 6, so we can multiply each accordingly:

3(5x + 2y = 9)

2(4x - 3y = 44)

Distribute:

15x + 6y = 27

8x - 6y = 88

Cancel using addition:

15x + 6y = 27

8x - 6y = 88

------------------

23x = 115

Divide:

x = 5.

Plug in this value of x into an equation to solve for y:

5(5) + 2y = 9

25 + 2y = 9

2y = -16

y = -8

The solution of the system is:

(5, -8).