How do you solve the system of equations y+ 3= 2x and y + 4= 3x?

May 14, 2018

$x = 1 , y = - 1$

Explanation:

Equation 1: $y + 3 = 2 x$
Equation 2: $y + 4 = 3 x$

Isolate the variable $y$ in equation 1, then plug that into equation 2.
$\setminus \textcolor{red}{y = 2 x - 3}$
$\setminus \textcolor{red}{y} + 4 = 3 x \setminus \rightarrow \left(\setminus \textcolor{red}{2 x - 3}\right) + 4 = 3 x$

Now simplify (add like terms, then solve for $x$)
$2 x + 1 = 3 x$
$\setminus \textcolor{b l u e}{1 = x}$

Plug the value of $x$ back into equation 1.
$y + 3 = 2 \setminus \textcolor{b l u e}{x} \setminus \rightarrow y + 3 = 2 \left(\setminus \textcolor{b l u e}{1}\right)$

Simplify to solve for $y$
$y = - 1$

Equation 1: (\color(red)(-1))+3\stackrel(?)(=)2(\color(blue)(1)) becomes $2 = 2$, so correct
Equation 2: (\color(red)(-1))+4\stackrel(?)(=)3(\color(blue)(1)) becomes $3 = 3$, so correct