How do you solve the system of equations #x+ 3y = - 14# and #2x - 4y = 30#?

1 Answer
Jim G.
May 26, 2018

#(x,y)to(17/5,-29/5)#

Explanation:

#x+3y=-14to(1)#

#2x-4y=30to(2)#

#"rearrange equation "(1)" expressing x in terms of y"#

#x=-14-3yto(3)#

#"substitute "x=-14-3y" into equation "(2)#

#2(-14-3y)-4y=30larrcolor(blue)"distribute"#

#-28-6y-4y=30larrcolor(blue)"simplify"#

#-28-10y=30#

#"add 28 to both sides"#

#-10y=58#

#"divide both sides by "-10#

#y=58/(-10)=-29/5#

#"substitute this value into equation "(3)" for x"#

#x=-14-(3xx-29/5)=-70/5+87/5=17/5#

#"solution is "(x,y)to(17/5,-29/5)#

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