Question

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

Short answer

The solution is$\left(4,-3\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$-3x-5y=3\cdots \cdots \left(1\right)$

$y=\frac{1}{2}x-5\cdots \cdots \left(2\right)$

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

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

Step 3. Solve for x

$\Rightarrow -3x-\frac{5}{2}x+25=3$

$\Rightarrow \frac{-6x-5x}{2}=3-25$

$\Rightarrow -\frac{11}{2}x=-22$

$\Rightarrow x=\frac{-44}{-11}$

$\Rightarrow x=4$

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

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

$\Rightarrow y=2-5$

$\Rightarrow y=-3$

Step 5. Checking solution 

Now we have $x=4$and$y=-3$

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

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

$\Rightarrow 3=3$

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

role="math" localid="1649087818803" $\Rightarrow -3=\frac{1}{2}\left(4\right)-5$

role="math" localid="1649087837741" $\Rightarrow -3=-3$