Answer
$x = 1$, $y = 3$, or $(1,3)$
Work Step by Step
Given:
$y = 4 - x$
$3x + y = 6$
Subtract the first equation, $y = 4 - x$, from the second equation,$3x + y = 6$:
$3x + y - (y) = 6 - (4 - x)
\\3x=6-(4-x)$
Subtract each term of the binomial to obtain:
$3x= 6 - 4 -(- x)
\\3x=6-4+x$
Combine like terms by subtracting $x$ on both sides:
$3x = 2 + x
\\3x-x=2+x-x
\\2x=2$
Divide both sides by $2$:
$x = 1$
Substitute $x = 1$ into the first equation, $y = 4-x$:
$y=4-x
\\y = 4- 1
\\y=3$
Thus, $x = 1$ and $y = 3$
