ANSWER
[tex]x=6,y=-2[/tex]
EXPLANATION
The given equations are:
[tex]3x - 2y = 22...(1)[/tex]
and
[tex]2x + 5y = 2...(2)[/tex]
Make x the subject of the second equation;
[tex]2x = 2 - 5y[/tex]
[tex]x = 1 - 2.5y...(3)[/tex]
Put equation (3) into equation (1).
[tex]3(1 - 2.5y) - 2y = 22[/tex]
[tex]3 - 7.5y- 2y = 22[/tex]
[tex]- 7.5y- 2y = 22 - 3[/tex]
[tex]- 9.5y = 19[/tex]
[tex]y = 19 \div - \frac{19}{2} [/tex]
[tex]y = 19 \times - \frac{2}{19} [/tex]
[tex]y = - 2[/tex]
Put y=-2 into equation (3) to get,
[tex]x = 1 - 2.5( - 2)[/tex]
[tex]x = 1 + 5 = 6[/tex]
Therefore the solution is
[tex]x=6,y=-2[/tex]
Checking for equation (1)
[tex]3(6)- 2( - 2) = 22[/tex]
[tex]18 + 4 = 22[/tex]
[tex]22= 22[/tex]
This is true.
Checking for equation (2)
[tex]2(6) + 5( - 2) = 2[/tex]
[tex]12 - 10 = 2[/tex]
[tex]2 = 2[/tex]
[tex] \boxed { \sqrt{} }CHECKED[/tex]
