Question

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

Short answer

The solution is$\left(5,-3\right)$

Step-by-step solution

Step 1. Given information 

The given equations are:

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

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

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

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

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

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

Step 3. Solve for y

$\Rightarrow -2-4y+3y=1$

$\Rightarrow -y=1+2$

$\Rightarrow -y=3$

$\Rightarrow y=-3$

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

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

$\Rightarrow x-6=-1$

$\Rightarrow x=-1+6$

$\Rightarrow x=5$

Step 5. Checking solution  

Now we have $x=5$and$y=-3$

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

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

$\Rightarrow -1=-1$

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

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

$\Rightarrow 1=1$