Solve the system of equations algebraically 5x - 3y = 6 6x - 4y = 2

Answer:[tex]x=9[/tex] and [tex]y=13[/tex]Step-by-step explanation:We have been given a system of equations. We are asked to solve our given system algebraically.[tex]5x-3y=6...(1)[/tex][tex]6x-4y=2...(2)[/tex] From equation (1), we will get:[tex]x=\frac{6+3y}{5}[/tex]Upon substituting this value in equation (2), we will get:[tex]6(\frac{6+3y}{5})-4y=2[/tex][tex]\frac{36+18y}{5}-4y=2[/tex][tex]\frac{36+18y}{5}-\frac{5*4y}{5}=2[/tex][tex]\frac{36+18y-20y}{5}=2[/tex][tex]\frac{36-2y}{5}=2[/tex][tex]\frac{36-2y}{5}*5=2*5[/tex][tex]36-2y=10[/tex][tex]36-36-2y=10-36[/tex][tex]-2y=-26[/tex][tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex][tex]y=13[/tex]Upon substituting [tex]y=13[/tex] in equation (1), we will get:[tex]5x-3(13)=6[/tex][tex]5x-39=6[/tex][tex]5x-39+39=6+39[/tex][tex]5x=45[/tex][tex]\frac{5x}{5}=\frac{45}{5}[/tex][tex]x=9[/tex]