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

ANSWER[tex]x=6,y=-2[/tex]EXPLANATIONThe 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]