Question

What is the solution to this system of equations?

4x + 5y = 7

3x – 2y = –12

Answer 1

x=-2,y=3

EXPLANATION

The system of equations is:

`4x + 5y = 7...(1)`

and

`3x - 2y = - 12...(2)`

We multiply the first equation by 2.5 to get:

`7.5x - 5y = - 30...(3)`

We add equations (1) and (3)

`4x+7.5x=-30+7`

`11.5x = - 23`

Divide both sides by 11.5

`x = - (23)/(11.5)`

`x = - 2`

Put x=-2 into the first equation or any other equation and solve for y.

`4( - 2) + 5y = 7`

`- 8 + 5y = 7`

`5y = 7 + 8`

`5y = 15`

`y = 3`

Answer 2

x = -2 and y = 3

Explanation:

It is given that,

4x + 5y = 7 ----(1)

3x – 2y = –12 ---(2)

To find the value of x and y

eq(1) * 3 ⇒

12x + 15y = 21 ----(3)

eq(2) * 4 ⇒

12x - 8y = -48 ---(4)

eq(3) - eq(4) ⇒

12x + 15y = 21 ----(3)

12x - 8y = -48 ---(4)

0 + 23y = 69

y = 69/23 = 3

y = 3

Substitute the value of y in eq(1)

4x + 5y = 7 ----(1)

4x + 5*3 = 7

4x = 7 - 15 = -8

x = -8/4 = -2

Therefore x = -2 and y = 3