Question

Solve each system of equations by the substitution method.

$8x+3y=26$

$2x=y–4$

Short answer

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

Step-by-step solution

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

Add 4 on both the sides of the $2x=y-4$and simplify.

$2x+4=y–4+4$

$2x+4=y$

Substitute $2x+4$for y into $8x+3y=26$and simplify.

$8x+3(2x+4)=26$

$8x+6x+12=26$

$14x+12=26$

Step 2. Solve for one variable.

Subtract 12 from both the sides of the equation obtained in step 2 and simplify.

$14x+12–12=26–12$

$14x=14$

Divide each side of the equation obtained in step 3 by 14 to find the value of x.

$\frac{14x}{14}=\frac{14}{14}$

$x=1$

Step 3. Solve for another variable.

Substitute 1 for into $2x=y-4$, to find the value of y.

$2\times 1=y-4$

$2=y-4$

$y=6$

Therefore, the solution of given system of equations is x = 1, y = 6.