How do you solve the following system using substitution?: 5x+2y=-4, -3x+y=205x+2y=−4,−3x+y=20

2 Answers
Jim G.
May 7, 2018

(x,y)to(-4,8)(x,y)→(−4,8)

Explanation:

5x+2y=-4to(1)5x+2y=−4→(1)

-3x+y=20to(2)−3x+y=20→(2)

"rearrange equation "(2)" to express y in terms of x"rearrange equation (2) to express y in terms of x

"add "3x" to both sides"add 3x to both sides

rArry=20+3xto(3)⇒y=20+3x→(3)

color(blue)"substitute "y=20+3x" into equation "(1)substitute y=20+3x into equation (1)

5x+2(20+3x)=-4larr"distribute"5x+2(20+3x)=−4←distribute

rArr5x+40+6x=-4⇒5x+40+6x=−4

rArr11x+40=-4⇒11x+40=−4

"subtract 40 from both sides"subtract 40 from both sides

rArr11x=-44⇒11x=−44

"divide both sides by 11"divide both sides by 11

rArrx=(-44)/11=-4⇒x=−4411=−4

"substitute "x=-4" into equation "(3)substitute x=−4 into equation (3)

rArry=20-12=8⇒y=20−12=8

"the point of intersection "=(-4,8)the point of intersection =(−4,8)

Narad T.
May 7, 2018

The solutions are {x=-4 ; y=8}{x=−4;y=8}

Explanation:

The equations are

{(5x+2y=-4),(-3x+y=20):}

<=>, {(5x+2y=-4),(y=3x+20):}

<=>, {(5x+2(3x+20)=-4),(y=3x+20):}

<=>, {(11x+40=-4),(y=3x+20):}

<=>, {(11x=-44),(y=3x+20):}

<=>, {(x=-4),(y=3xx-4+20=8):}

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