Solve the system of equations. \begin{aligned} &-5y+6x = 40 \\\\ &3y-8x=-46 \end{aligned} ​ −5y+6x=40 3y−8x=−46 ​ x=x=x, equals y=y=y, equals

Answer:The solution is [tex](5,-2)[/tex] that is, [tex]x=5[/tex] and [tex]y=-2[/tex]Step-by-step explanation:The given system of equations is[tex]\left \{ {{-5y+6x=40} \atop {3y-8x=-46}} \right.[/tex]We can solve this system by elimination, that is, we have to eliminate one variable to find the other one.We are gonna multiply the second equation by [tex]\frac{6}{8}[/tex] and solve for [tex]y[/tex][tex]\left \{ {{-5y+6x=40} \atop {\frac{18}{8} y-6x=-\frac{276}{8} }} \right.\\\\-5y + \frac{18}{8}y=40-\frac{276}{8}\\-5y+\frac{9}{4}y=40-\frac{69}{2}\\\frac{-20y+9y}{4}=\frac{80-69}{2}\\ \frac{-11y}{4}=\frac{11}{2} \\y=\frac{4(11)}{2(-11)} \\y=-2[/tex]Now, we replace this value in one equation to find the other value[tex]-5y+6x=40\\-5(-2)+6x=40\\10+6x=40\\6x=40-10\\x=\frac{30}{6}=5[/tex]Therefore, the solution is [tex](5,-2)[/tex] that is, [tex]x=5[/tex] and [tex]y=-2[/tex]