How do you solve the system of equations $3x+2y = 14$ and $y = x+2$ by substitution?

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Answer 1 · 2017-08-12T21:52:29

See a solution process below:

Step 1) Because the second equation is already solved for $y$ we can substitute $(x + 2)$ for $y$ in the first equation and solve for $x$ :

$3x + 2y = 14$ becomes:

$3x + 2(x + 2) = 14$

$3x + (2 xx x) + (2 xx 2) = 14$

$3x + 2x + 4 = 14$

$(3 + 2)x + 4 = 14$

$5x + 4 = 14$

$5x + 4 - color(red)(4) = 14 - color(red)(4)$

$5x + 0 = 10$

$5x = 10$

$(5x)/color(red)(5) = 10/color(red)(5)$

$(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 2$

$x = 2$

Step 2) Substitute $2$ for $x$ in the second solution and solve for $y$ :

$y = x + 2$ becomes:

$y = 2 + 2$

$y = 4$

The Solution Is: $x = 2$ and $y = 4$ or $(2, 4)$

How do you solve the system of equations 3x+2y = 143x+2y = 14 and y = x+2y = x+2 by substitution?