Solve the System of Equations 3y-6x=24 8+2x=y

$3 y - 6 x = 24$ $8 + 2 x = y$

Step 1

Rewrite the equation as $y = 8 + 2 x$ .

$y = 8 + 2 x$

$3 y - 6 x = 24$

Step 2

Replace all occurrences of $y$ with $8 + 2 x$ in each equation.

Replace all occurrences of $y$ in $3 y - 6 x = 24$ with $8 + 2 x$ .

$3 (8 + 2 x) - 6 x = 24$

$y = 8 + 2 x$

Simplify the left side.

Simplify $3 (8 + 2 x) - 6 x$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 8 + 3 (2 x) - 6 x = 24$

$y = 8 + 2 x$

Multiply $3$ by $8$ .

$24 + 3 (2 x) - 6 x = 24$

$y = 8 + 2 x$

Multiply $2$ by $3$ .

$24 + 6 x - 6 x = 24$

$y = 8 + 2 x$

$24 + 6 x - 6 x = 24$

$y = 8 + 2 x$

Combine the opposite terms in $24 + 6 x - 6 x$ .

Subtract $6 x$ from $6 x$ .

$24 + 0 = 24$

$y = 8 + 2 x$

Add $24$ and $0$ .

$24 = 24$

$y = 8 + 2 x$

$24 = 24$

$y = 8 + 2 x$

$24 = 24$

$y = 8 + 2 x$

$24 = 24$

$y = 8 + 2 x$

$24 = 24$

$y = 8 + 2 x$

Step 3

Remove any equations from the system that are always true.

$y = 8 + 2 x$

Step 4