Solve the following system of equations3x - 2y =55-2x - 3y = 14

Accepted Solution

Answer:The solution is:[tex](\frac{137}{13}, -\frac{152}{13})[/tex]Step-by-step explanation:We have the following equations[tex]3x - 2y =55[/tex][tex]-2x - 3y = 14[/tex]To solve the system multiply by [tex]\frac{3}{2}[/tex] the second equation and add it to the first equation[tex]-2*\frac{3}{2}x - 3\frac{3}{2}y = 14\frac{3}{2}[/tex][tex]-3x - \frac{9}{2}y = 21[/tex][tex]3x - 2y =55[/tex]---------------------------------------[tex]-\frac{13}{2}y=76[/tex][tex]y=-76*\frac{2}{13}[/tex][tex]y=-\frac{152}{13}[/tex]Now substitute the value of y in any of the two equations and solve for x[tex]-2x - 3(-\frac{152}{13}) = 14[/tex][tex]-2x +\frac{456}{13} = 14[/tex][tex]-2x= 14-\frac{456}{13}[/tex][tex]-2x=-\frac{274}{13}[/tex][tex]x=\frac{137}{13}[/tex]The solution is:[tex](\frac{137}{13}, -\frac{152}{13})[/tex]