Solve by Substitution 6x-3y=5 y-2x=8

$6 x - 3 y = 5$ $y - 2 x = 8$

Step 1

Add $2 x$ to both sides of the equation.

$y = 8 + 2 x$

$6 x - 3 y = 5$

Step 2

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

Replace all occurrences of $y$ in $6 x - 3 y = 5$ with $8 + 2 x$ .

$6 x - 3 (8 + 2 x) = 5$

$y = 8 + 2 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$6 x - 3 \cdot 8 - 3 (2 x) = 5$

$y = 8 + 2 x$

Multiply $- 3$ by $8$ .

$6 x - 24 - 3 (2 x) = 5$

$y = 8 + 2 x$

Multiply $2$ by $- 3$ .

$6 x - 24 - 6 x = 5$

$y = 8 + 2 x$

$6 x - 24 - 6 x = 5$

$y = 8 + 2 x$

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

Subtract $6 x$ from $6 x$ .

$0 - 24 = 5$

$y = 8 + 2 x$

Subtract $24$ from $0$ .

$- 24 = 5$

$y = 8 + 2 x$

$- 24 = 5$

$y = 8 + 2 x$

$- 24 = 5$

$y = 8 + 2 x$

$- 24 = 5$

$y = 8 + 2 x$

$- 24 = 5$

$y = 8 + 2 x$

Step 3

Since $- 24 = 5$ is not true, there is no solution.

No solution

Step 4