Question

What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12 The solution is (–2, 3)(3, –1)X (7, 3)(13, –9).

Answer 1

For this case we have two systems of equations with two unknowns.

`4x + 5y = 7\\3x-2y = -12`

We multiply the first equation by -3, the second by 4:

`-12x-15y = -21\\12x-8y = -48`

We add both equations:

`-23y = -69\\y = \frac {69} {23}\\y = 3`

We substitute the value of y into any of the equations and clear the value of x.

`4x + 5 (3) = 7\\4x + 15 = 7\\4x = 7-15\\4x = -8\\x = \frac {-8} {4}\\x = -2`

Answer:

(-2,3)

Option A