Question 10 of 211 PointUse the elimination method to solve the system of equations. Choose thecorrect ordered pair.10x +2y = 643x - 4y = -36A. (4,12)B. (-3, 11)C. (2,10)D. (-5, 8)
Accepted Solution
A:
ANSWERA. (4,12)EXPLANATIONThe equations are:[tex]10x +2y = 64...(1)[/tex]and[tex]3x - 4y = -36...(2)[/tex]To eliminate a variable we make the coefficients of that variable the same in both equations.It is easier to eliminate x.We multiply the first equation by 2 to get:[tex]20x + 4y = 128...(3)[/tex]We add equations (2) and (3).[tex]3x + 20x + 4y - 4y = - 36 + 128[/tex][tex]23x = 92[/tex]Divide both sides by 23[tex] \frac{23x}{23} = \frac{92}{23} [/tex][tex]x = 4[/tex]Put x=4 into equation (1).[tex]10(4)+2y = 64[/tex][tex]40+2y = 64[/tex][tex]2y = 64 - 40[/tex][tex]2y = 24[/tex][tex] \frac{2y}{2} = \frac{24}{2} [/tex][tex]y = 12[/tex]The solution is (4,12)