# How do you solve the following system of equations?: 4x – y = 14 , 7x + 3y=10?

Mar 9, 2017

See the entire solution process below:

#### Explanation:

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

$4 x - y = 14$

$4 x - y + \textcolor{red}{y} - \textcolor{b l u e}{14} = 14 + \textcolor{red}{y} - \textcolor{b l u e}{14}$

$4 x - 0 - \textcolor{b l u e}{14} = 14 - \textcolor{b l u e}{14} + y$

$4 x - 14 = 0 + y$

$4 x - 14 = y$

$y = 4 x - 14$

Step 2) Substitute $4 x - 14$ for $y$ in the second equation and solve for $x$:

$7 x + 3 y = 10$ becomes:

$7 x + 3 \left(4 x - 14\right) = 10$

$7 x + \left(3 \times 4 x\right) - \left(3 \times 14\right) = 10$

$7 x + 12 x - 42 = 10$

$19 x - 42 = 10$

$19 x - 42 + \textcolor{red}{42} = 10 + \textcolor{red}{42}$

$19 x - 0 = 52$

$19 x = 52$

$\frac{19 x}{\textcolor{red}{19}} = \frac{52}{\textcolor{red}{19}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{19}}} x}{\cancel{\textcolor{red}{19}}} = \frac{52}{19}$

$x = \frac{52}{19}$

Step 3) Substitute $\frac{52}{49}$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = 4 x - 14$ becomes:

$y = \left(4 \times \frac{52}{19}\right) - 14$

$y = \frac{208}{19} - \left(\frac{19}{19} \times 14\right)$

$y = \frac{208}{19} - \frac{266}{19}$

$y = - \frac{58}{49}$

The solution is: $x = \frac{52}{19}$ and $y = - \frac{58}{49} \mathmr{and}$(52/19, -58/49)#