How do you use substitution to solve the system of equations $y=7x+8$ and $y=x+20$ ?

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Answer 1 · 2017-06-04T19:10:11

See a solution process below:

Step 1) Because the first equation is already solved for $y$ we can substitute $(7x + 8)$ for $y$ in the second equation and solve for $x$ :

$y = x + 20$ becomes:

$7x + 8 = x + 20$

$-color(blue)(x) + 7x + 8 - color(red)(8) = -color(blue)(x) + x + 20 - color(red)(8)$

$-color(blue)(1x) + 7x + 0 = 0 + 12$

$(-color(blue)(1) + 7)x = 12$

$6x = 12$

$(6x)/color(red)(6) = 12/color(red)(6)$

$(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) = 2$

$x = 2$

Step 2) Substitute $2$ for $x$ in the first equation and calculate $y$ :

$y = 7x + 8$ becomes:

$y = (7 xx 2) + 8$

$y = 14 + 8$

$y = 22$

The solution is: $x = 2$ and $y = 22$ or $(2, 22)$

How do you use substitution to solve the system of equations y=7x+8y=7x+8 and y=x+20y=x+20?