Solve the System of Equations y=2x-3 2x=y-3

$y = 2 x - 3$ $2 x = y - 3$

Step 1

Replace all occurrences of $y$ with $2 x - 3$ in each equation.

Replace all occurrences of $y$ in $2 x = y - 3$ with $2 x - 3$ .

$2 x = (2 x - 3) - 3$

$y = 2 x - 3$

Simplify the right side.

Subtract $3$ from $- 3$ .

$2 x = 2 x - 6$

$y = 2 x - 3$

$2 x = 2 x - 6$

$y = 2 x - 3$

$2 x = 2 x - 6$

$y = 2 x - 3$

Step 2

Solve for $x$ in $2 x = 2 x - 6$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$2 x - 2 x = - 6$

$y = 2 x - 3$

Subtract $2 x$ from $2 x$ .

$0 = - 6$

$y = 2 x - 3$

$0 = - 6$

$y = 2 x - 3$

Since $0 \neq - 6$ , there are no solutions.

No solution

$y = 2 x - 3$

No solution

Step 3