# How do solve the following linear system?:  2x-y=4 , 7x+3y=27 ?

Jun 19, 2018

See a solution process below:

#### Explanation:

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

$2 x - y = 4$

$2 x - \textcolor{b l u e}{4} - y + \textcolor{red}{y} = 4 - \textcolor{b l u e}{4} + \textcolor{red}{y}$

$2 x - 4 - 0 = 0 + y$

$2 x - 4 = y$

$y = 2 x - 4$

Step 2) Substitute $\left(2 x - 4\right)$ for $y$ in the second equation and solve for $x$:

$7 x + 3 y = 27$ becomes:

$7 x + 3 \left(2 x - 4\right) = 27$

$7 x + \left(3 \times 2 x\right) - \left(3 \times 4\right) = 27$

$7 x + 6 x - 12 = 27$

$\left(7 + 6\right) x - 12 = 27$

$13 x - 12 = 27$

$13 x - 12 + \textcolor{red}{12} = 27 + \textcolor{red}{12}$

$13 x - 0 = 39$

$13 x = 39$

$\frac{13 x}{\textcolor{red}{13}} = \frac{39}{\textcolor{red}{13}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{13}}} x}{\cancel{\textcolor{red}{13}}} = 3$

$x = 3$

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

$y = 2 x - 4$ becomes:

$y = \left(2 \times 3\right) - 4$

$y = 6 - 4$

$y = 2$

The Solution Is:

$x = 3$ and $y = 2$

Or

$\left(3 , 2\right)$