Question

Solve each system of equations by the substitution method.

$x–7y=13$

$3x–5y=23$

Short answer

The solution of given system of equations is x = 6, y = – 1.

Step-by-step solution

Step 1. Substitute value of one variable from one equation to another.

Add 7y on both the sides of $x-7y=13$and simplify.

$x-7y+7y=13+7y$

$x=13+7y$

Substitute $13+7y$for into $3x-5y=23$and simplify.

$3\left(13+7y\right)-5y=23$

$39+21y-5y=23$

$39+16y=23$

$16y=-16$

Step 2. Solve for one variable.

Divide each side of the equation obtained in step 2 by 16 to find the value of y.

$\frac{16y}{16}=\frac{-16}{16}$

$y=-1$

Step 3. Solve for another variable.

Substitute $-1$for into $x-7y=13$, to find the value of x.

$x-7\left(-1\right)=13$

$x+7=13$

$x=6$

Therefore, the solution of given system of equations isx = 6, y = – 1.