# How do solve the following linear system?:  7x+2y=2 , 8x+2y=3 ?

May 24, 2018

The solution is $\left\{\begin{matrix}y = - \frac{5}{2} \\ x = 1\end{matrix}\right.$

#### Explanation:

Solve the equations as follows

$\left\{\begin{matrix}7 x + 2 y = 2 \\ 8 x + 2 y = 3\end{matrix}\right.$

$\left(2\right) - \left(1\right)$, $\implies$, $\left\{\begin{matrix}7 x + 2 y = 2 \\ x = 1\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}y = \frac{2 - 7 x}{2} \\ x = 1\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}y = \frac{2 - 7}{2} \\ x = 1\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}y = - \frac{5}{2} \\ x = 1\end{matrix}\right.$

May 24, 2018

See explanation.

#### Explanation:

The original system is:

## $\left\{\begin{matrix}7 x + 2 y = 2 \\ 8 x + 2 y = 3\end{matrix}\right.$

We can easily notice that $y$ has the same coefficient in both equations, so if we multiply any of the equations by $- 1$ the coefficients will be opposite numbers. I multiplied the first equation and got:

## $\left\{\begin{matrix}- 7 x - 2 y = - 2 \\ 8 x + 2 y = 3\end{matrix}\right.$

Now if we add both sides of the equations we get an equation with one variable only ($x$):

## $x = 1$

Now we have to substitute the calculated value of $x$ to calculate $y$:

## $y = - 2.5$

The solution of the system is: