Question

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

Short answer

The solution is$\left(-5,2\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

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

$3x+5y=-5\cdots \cdots \left(2\right)$

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

From equation $\left(1\right)$, $x=1-3y$

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

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

Step 3. Solve for y

$\Rightarrow 3-9y+5y=-5$

$\Rightarrow -4y=-5-3$

$\Rightarrow -4y=-8$

$\Rightarrow y=\frac{-8}{-4}$

$\Rightarrow y=2$

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

$\Rightarrow x+3\left(2\right)=1$

$\Rightarrow x+6=1$

$\Rightarrow x=1-6$

$\Rightarrow x=-5$

Step 5. Checking solution  

Now we have$x=-5$ and$y=2$

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

$\Rightarrow -5+3\left(2\right)=1$

$\Rightarrow 1=1$

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

$\Rightarrow 3\left(-5\right)+5\left(2\right)=-5$

$\Rightarrow -5=-5$