How do you solve $3x+4y=-4$ and $x+2y=2$ using substitution?

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Answer 1 · 2017-01-24T14:48:49

See the entire solution process below:

Step 1) Solve the second equation for $x$ :

$x + 2y = 2$

$x + 2y - 2y = 2 - 2y$

$x + 0 = 2 - 2y$

$x = 2 - 2y$

Step 2) Substitute $color(red)(2 - 2y)$ for $x$ in the first equation and solve for $y$ :

$3(color(red)(2 - 2y)) + 4y = -4$

$6 - 6y + 4y = -4$

$6 - 2y = -4$

$6 - 6 - 2y = -4 - 6$

$0 - 2y = -10$

$-2y = -10$

$(-2y)/color(red)(-2) = (-10)/color(red)(-2)$

$(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 5$

$y = 5$

Step 3) Substitute $color(red)(5)$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$ :

$x = 2 - (2 xx color(red)(5))$

$x = 2 - 10$

$x = -8$

The solution is:

$x = -8$ and $y = 5$ or (-8, 5)

How do you solve 3x+4y=-43x+4y=-4 and x+2y=2x+2y=2 using substitution?