Find the solution to the system of linear equations y = 5x + 4 and y = −3x + 12 using the intersection method. Check your answer.(x, y) =

Answer:The solution to the system of linear equations is (1,9).Step-by-step explanation:The given system of linear equations[tex]y=5x+4[/tex]            ... (1)[tex]y=-3x+12[/tex]           .... (2)Subtract equation (2) from equation (1) to eliminate y.[tex]y-y=(5x+4)-(-3x+12)[/tex] [tex]0=5x+4+3x-12[/tex] On combining like terms, we get[tex]0=(5x+3x)+(4-12)[/tex] [tex]0=8x-8[/tex] Add 8 on both sides.[tex]0+8=8x-8+8[/tex] [tex]8=8x[/tex]Divide both sides by 8.[tex]1=x[/tex]The value of x is 1.Substitute x=1 in equation (1).[tex]y=5(1)+4[/tex][tex]y=5+4[/tex][tex]y=9[/tex]The value of y is 9.Therefore the solution to the system of linear equations is (1,9).