Solve the System of Equations 2y=4x+6 y=2x+6

$2 y = 4 x + 6$ $y = 2 x + 6$

Step 1

Replace all occurrences of $y$ with $2 x + 6$ in each equation.

Replace all occurrences of $y$ in $2 y = 4 x + 6$ with $2 x + 6$ .

$2 (2 x + 6) = 4 x + 6$

$y = 2 x + 6$

Simplify the left side.

Simplify $2 (2 x + 6)$ .

Apply the distributive property.

$2 (2 x) + 2 \cdot 6 = 4 x + 6$

$y = 2 x + 6$

Multiply.

Multiply $2$ by $2$ .

$4 x + 2 \cdot 6 = 4 x + 6$

$y = 2 x + 6$

Multiply $2$ by $6$ .

$4 x + 12 = 4 x + 6$

$y = 2 x + 6$

$4 x + 12 = 4 x + 6$

$y = 2 x + 6$

$4 x + 12 = 4 x + 6$

$y = 2 x + 6$

$4 x + 12 = 4 x + 6$

$y = 2 x + 6$

$4 x + 12 = 4 x + 6$

$y = 2 x + 6$

Step 2

Solve for $x$ in $4 x + 12 = 4 x + 6$ .

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

Subtract $4 x$ from both sides of the equation.

$4 x + 12 - 4 x = 6$

$y = 2 x + 6$

Combine the opposite terms in $4 x + 12 - 4 x$ .

Subtract $4 x$ from $4 x$ .

$0 + 12 = 6$

$y = 2 x + 6$

Add $0$ and $12$ .

$12 = 6$

$y = 2 x + 6$

$12 = 6$

$y = 2 x + 6$

$12 = 6$

$y = 2 x + 6$

Since $12 \neq 6$ , there are no solutions.

No solution

$y = 2 x + 6$

No solution

Step 3

Solve the System of Equations 2y=4x+6 y=2x+6

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