Question

Solve the system of equation$\left\{\begin{array}{l}2x+y=5\\ x-2y=-15\end{array}\right.$by substitution

Short answer

The solution is$\left(-1,7\right)$

Step-by-step solution

Step 1. Given information 

The given equations are:

$2x+y=5\cdots \cdots \left(1\right)$

$x-2y=-15\cdots \cdots \left(2\right)$

Step 2. Substitute value of y from equation 1 in equation 2

From equation $\left(1\right)$, $y=5-2x$

Put in equation $\left(2\right)$

$\Rightarrow x-2\left(5-2x\right)=-15$

Step 3. Solve for x

$\Rightarrow x-10+4x=-15$

$\Rightarrow 5x=-15+10$

$\Rightarrow 5x=-5$

$\Rightarrow x=\frac{-5}{5}$

$\Rightarrow x=-1$

Step 4. Substitute value of x from step 3 in equation 2

$\Rightarrow -1-2y=-15$

$\Rightarrow -2y=-14$

$\Rightarrow y=\frac{-14}{-2}$

$\Rightarrow y=7$

Step 5. Checking solution  

Now we have $x=-1$and$y=7$

Put these values in equation $\left(1\right)$

$\Rightarrow 2\left(-1\right)+7=5$

$\Rightarrow 5=5$

Also put these values in equation $\left(7\right)$

$\Rightarrow -1-2\left(7\right)=-15$

$\Rightarrow -15=-15$