Question

Solve the system of equation$\left\{\begin{array}{l}3x+y=1\\ -4x+y=15\end{array}\right.$by substitution

Short answer

The solution is$\left(-2,7\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

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

$-4x+y=15\cdots \cdots \left(2\right)$

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

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

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

$\Rightarrow -4x+1-3x=15$

Step 3. Solve for x

$\Rightarrow -7x=15-1$

$\Rightarrow -7x=14$

$\Rightarrow x=-\frac{14}{7}$

$\Rightarrow x=-2$

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

$\Rightarrow -4\left(-2\right)+y=15$

$\Rightarrow 8+y=15$

$\Rightarrow y=15-8$

$\Rightarrow y=7$

Step 5. Checking solution 

Now we have $x=-2$and $y=7$

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

$\Rightarrow 3\left(-2\right)+7=1$

$\Rightarrow 1=1$

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

$\Rightarrow -4\left(-2\right)+7=15$

$\Rightarrow 15=15$