Question

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

Short answer

The solution is$\left(6,-3\right)$.

Step-by-step solution

Step 1. Given information

The given equations are:

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

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

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

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

Step 3. Solve for x

$\Rightarrow 2x-3x+9=3$

$\Rightarrow -x=3-9$

$\Rightarrow -x=-6$

$\Rightarrow x=6$

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

$\Rightarrow y=-6+3$

$\Rightarrow y=-3$

Step 5. Checking solution

Now we have $x=6$and $y=-3$

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

$\Rightarrow 2\left(6\right)+3\left(-3\right)=3$

$\Rightarrow 3=3$

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

$\Rightarrow -3=-6+3$

$\Rightarrow -3=-3$