# 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]}