Question

Solve the system of equation$\left\{\begin{array}{l}3x+4y=1\\ y=-\frac{2}{5}x+2\end{array}\right.$by substitution

Short answer

The solution is$\left(-5,4\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$3x+4y=1\cdots \cdots \left(1\right)$

$y=-\frac{2}{5}x+2\cdots \cdots \left(2\right)$

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

$\Rightarrow 3x+4\left(-\frac{2}{5}x+2\right)=1$

Step 3. Solve for x

$\Rightarrow 3x-\frac{8}{5}x+8=1$

$\Rightarrow \frac{15x-8x}{5}=1-8$

$\Rightarrow \frac{7x}{5}=-7$

" width="9" height="19" role="math">⇒7x=-35

$\Rightarrow x=-\frac{35}{7}$

$\Rightarrow x=-5$

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

$\Rightarrow y=-\frac{2}{5}\left(-5\right)+2$

$\Rightarrow y=2+2$

$\Rightarrow y=4$

Step 5. Checking solution 

Now we have $x=-5$and $y=4$

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

$\Rightarrow 3\left(-5\right)+4\left(4\right)=1$

$\Rightarrow 1=1$

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

$\Rightarrow 4=-\frac{2}{5}\left(-5\right)+2$

$\Rightarrow 4=4$