How do you solve the following linear system:  -x + y = 3, 5x-2y=11 ?

Jun 14, 2018

See a solution process below:

Explanation:

Step 1) Solve the first equation for $y$:

$- x + y = 3$

$- x + \textcolor{red}{x} + y = 3 + \textcolor{red}{x}$

$0 + y = 3 + x$

$y = 3 + x$

Step 2) Substitute $\left(3 + x\right)$ for $y$ in the second equation and solve for $x$:

$5 x - 2 y = 11$ becomes:

$5 x - 2 \left(3 + x\right) = 11$

$5 x - \left(2 \cdot 3\right) - \left(2 \cdot x\right) = 11$

$5 x - 6 - 2 x = 11$

$5 x - 6 + \textcolor{red}{6} - 2 x = 11 + \textcolor{red}{6}$

$5 x - 0 - 2 x = 17$

$5 x - 2 x = 17$

$\left(5 - 2\right) x = 17$

$3 x = 17$

$\frac{3 x}{\textcolor{red}{3}} = \frac{17}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = \frac{17}{3}$

$x = \frac{17}{3}$

Step 3) Substitute $\frac{17}{3}$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = 3 + x$ becomes:

$y = 3 + \frac{17}{3}$

$y = \left(\frac{3}{3} \cdot 3\right) + \frac{17}{3}$

$y = \frac{9}{3} + \frac{17}{3}$

$y = \frac{26}{3}$

The Solution Is:

$x = \frac{17}{3}$ and $y = \frac{26}{3}$

Or

$\left(\frac{17}{3} , \frac{26}{3}\right)$