Question

Solve the system of equation$\left\{\begin{array}{l}2x+y=10\\ -x+y=-5\end{array}\right.$by substitution

Short answer

The solution is $\left(5,0\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$2x+y=10\cdots \cdots \left(1\right)$

role="math" localid="1647769799174" $-x+y=-5\cdots \cdots \left(2\right)$

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

From equation $\left(1\right)$, $y=10-2x$

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

$\Rightarrow -x+10-2x=-5$

Step 3. Solve for x

$\Rightarrow -3x=-5-10$

$\Rightarrow -3x=-15$

$\Rightarrow x=5$

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

$\Rightarrow -5+y=-5$

$\Rightarrow y=-5+5$

$\Rightarrow y=0$

Step 5. Checking solution 

Now we have $x=5$and$y=0$

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

$\Rightarrow 2\left(5\right)+0=10$

$\Rightarrow 10=10$

Also put these values in equation $\left(2\right)$

$\Rightarrow -5+0=-5$

$\Rightarrow -5=-5$