Question

Solve the following system of equations algebraically and check: 3x-2y=22
2x+5y=2

Answer 1

`x=6,y=-2`

Step-by-step explanation

The given equations are:

`3x - 2y = 22...(1)`

and

`2x + 5y = 2...(2)`

Make x the subject of the second equation;

`2x = 2 - 5y`

`x = 1 - 2.5y...(3)`

Put equation (3) into equation (1).

`3(1 - 2.5y) - 2y = 22`

`3 - 7.5y- 2y = 22`

`- 7.5y- 2y = 22 - 3`

`- 9.5y = 19`

`y = 19 / - (19)/(2)`

`y = 19 * - (2)/(19)`

`y = - 2`

Put y=-2 into equation (3) to get,

`x = 1 - 2.5( - 2)`

`x = 1 + 5 = 6`

Therefore the solution is

`x=6,y=-2`

Checking for equation (1)

`3(6)- 2( - 2) = 22`

`18 + 4 = 22`

`22= 22`

This is true.

Checking for equation (2)

`2(6) + 5( - 2) = 2`

`12 - 10 = 2`

`2 = 2`

`\boxed { \sqrt{} }CHECKED`