Solve the system algebraically. Check your work. 5x + 2y = 10 3x + 2y = 6 ANSWER: {( a0)}I need a 100% right answer14 pts.

Answer:[tex]x=2[/tex], [tex]y=0[/tex], or as an ordered pair [tex](x,y)=(2,0)[/tex].Step-by-step explanation:We have the system of equations[tex]5x + 2y = 10[/tex] equation (1)[tex]3x + 2y = 6[/tex] equation (2) Since both equations have the term [tex]2y[/tex], we are using the elimination method:Step 1. Multiply equation (2) by -1 and add the result equation to equation (1):[tex]\left \{ {{-1(3x + 2y = 6)} \atop +{5x + 2y = 10}} \right.[/tex][tex]\left \{ {{-3x -2y = -6)} \atop +{5x + 2y = 10}} \right.[/tex]Now we can get rid of [tex]-2y[/tex][tex]2x=4[/tex][tex]x=\frac{4}{2}[/tex][tex]x=2[/tex] Step 2. Replace the value [tex]x=2[/tex] in equation (1) to find the value of [tex]y[/tex]:[tex]5x + 2y = 10[/tex][tex]5(2) + 2y = 10[/tex][tex]10 + 2y = 10[/tex][tex]2y = 0[/tex][tex]y = 0[/tex]We can conclude that the solution of the system of equations is [tex]x=2[/tex], [tex]y=0[/tex], or as an ordered pair [tex](x,y)=(2,0)[/tex].