Question

Solve the system of equation$\left\{\begin{array}{l}4x+y=10\\ x-2y=-20\end{array}\right.$by substitution

Short answer

The solution is$\left(0,10\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$4x+y=10\cdots \cdots \left(1\right)$

$x-2y=-20\cdots \cdots \left(2\right)$

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

From equation $\left(1\right)$, $y=10-4x$

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

$\Rightarrow x-2\left(10-4x\right)=-20$

 Step 3. Solve for x

$\Rightarrow x-20+8x=-20$

$\Rightarrow 9x=-20+20$

$\Rightarrow 9x=0$

$\Rightarrow x=0$

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

$\Rightarrow 0-2y=-20$

$\Rightarrow y=\frac{-20}{-2}$

$\Rightarrow y=10$

Step 5. Checking solution  

Now we have $x=0$and$y=10$

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

$\Rightarrow 4\left(0\right)+10=10$

$\Rightarrow 10=10$

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

$\Rightarrow 0-2\left(10\right)=-20$

$\Rightarrow -20=-20$