Question

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

Answer 1

ANSWER

$x=6,y=-2$

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).

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

$3 - 7.5y- 2y = 22$

$- 7.5y- 2y = 22 - 3$

$- 9.5y = 19$

$y = 19 \div - \frac{19}{2}$

$y = 19 \times - \frac{2}{19}$

$y = - 2$

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)

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

$12 - 10 = 2$

$2 = 2$

$\boxed { \sqrt{} }CHECKED$