How do you solve this system of equations: #2x + 4y = 9; 5x - y = - \frac { 21} { 2}#?
1 Answer
Jan 31, 2018
Explanation:
#2x+4y=9to(1)#
#5x-y=-21/2to(2)#
#"multiply equation "(2)" by 4"#
#"this will make the coefficients of y opposites so we can"#
#"add the equations and eliminate the y term"#
#rArr20x-4y=-42to(3)#
#"add equations "(1)" and "(3)" term by term to eliminate y"#
#(2x+20x)+(cancel(4y-4y)^0)=(9-42)#
#rArr22x=-33#
#"divide both sides by 22"#
#(cancel(22) x)/cancel(22)=(-33)/22#
#rArrx=-3/2#
#"substitute "x=-3/2" in equation "(1)" and solve for y"#
#-3+4y=9#
#"add 3 to both sides"#
#cancel(-3)cancel(+3)+4y=9+3#
#rArr4y=12#
#"divide both sides by 4"#
#(cancel(4) y)/cancel(4)=12/4#
#rArry=3#
#"the point of intersection is "(-3/2,3)#
graph{(y+1/2x-9/4)(y-5x-21/2)((x+3/2)^2+(y-3)^2-0.04)=0 [-10, 10, -5, 5]}