How do solve the following linear system?: $5 x + 2 y = 4, y = - 3 x + 4$ $5x+2y=4 , y=-3x+4$ ?

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Answer 1 · 2018-03-11T22:54:14

$x = 4, y = - 8$ $x=4, y=-8$

$5 x + 2 y = 4$ $5x+2y=4$
$y = - 3 x + 4$ $y=-3x+4$

Since the second function already has the y term isolated, plug it in for y in the first function to solve for x

$5 x + 2 (- 3 x + 4) = 4$ $5x+2(-3x+4)=4$ (Distribute the 2)

$5 x - 6 x + 8 = 4$ $5x-6x+8=4$ (Combine like terms)

$- x + 8 = 4$ $-x+8=4$ (Subtract 8 from both sides)

$- x = - 4$ $-x=-4$ (Divide both sides by -1)

$x = 4$ $x=4$

Now that you found the x variable, plug it into either equation to find y

$y = - 3 (4) + 4$ $y=-3(4)+4$ (Distribute -3)

$y = - 12 + 4$ $y=-12+4$ (Find the difference/sum)

$y = - 8$ $y=-8$

Check your answer by plugging it back into either of the original equations

$5 (4) + 2 (- 8) = 4$ $5(4)+2(-8)=4$

$20 + (- 16) = 4$ $20+(-16)=4$

$4 = 4$ $4=4$

This is how you solve by substitution

How do solve the following linear system?: 5x+2y=4 , y=-3x+4 5x+2y=4,y=−3x+4 5x+2y=4 , y=-3x+4 ?