Question

Solve the system of equation$\left\{\begin{array}{l}4x+2y=8\\ 8x-y=1\end{array}\right.$by substitution

Short answer

The soluion is$\left(0.5,3\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$4x+2y=8\cdots \cdots \left(1\right)$

$8x-y=1\cdots \cdots \left(2\right)$

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

From equation $\left(2\right)$$y=8x-1$

Substitute in equation $\left(1\right)$

$\Rightarrow 4x+2\left(8x-1\right)=8$

Step 3. Solve for x

$\Rightarrow 4x+16x-2=8$

$\Rightarrow 20x=10$

$\Rightarrow x=\frac{10}{20}$

$\Rightarrow x=0.5$

Step 4. Substitute value of x from step 3 in equation 1

$\Rightarrow 4\left(0.5\right)+2y=8$

$\Rightarrow 2+2y=8$

$\Rightarrow 2y=6$

$\Rightarrow y=3$

Step 5. Checking solution

Now we have $x=0.5$and $y=3$

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

localid="1649345126722" $\Rightarrow 4\left(0.5\right)+2\left(3\right)=8$

$\Rightarrow 8=8$

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

$\Rightarrow 8\left(0.5\right)-3=1$

$\Rightarrow 1=1$