Solve by Substitution y=2x+3 and 2y-2x=8

$y = 2 x + 3$ and $2 y - 2 x = 8$

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

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

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

$y = 2 x + 3$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = 2 x + 3$

Multiply $2$ by $2$ .

$4 x + 2 \cdot 3 - 2 x = 8$

$y = 2 x + 3$

Multiply $2$ by $3$ .

$4 x + 6 - 2 x = 8$

$y = 2 x + 3$

$4 x + 6 - 2 x = 8$

$y = 2 x + 3$

Subtract $2 x$ from $4 x$ .

$2 x + 6 = 8$

$y = 2 x + 3$

$2 x + 6 = 8$

$y = 2 x + 3$

$2 x + 6 = 8$

$y = 2 x + 3$

$2 x + 6 = 8$

$y = 2 x + 3$

Solve for $x$ in $2 x + 6 = 8$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$2 x = 8 - 6$

$y = 2 x + 3$

Subtract $6$ from $8$ .

$2 x = 2$

$y = 2 x + 3$

$2 x = 2$

$y = 2 x + 3$

Divide each term in $2 x = 2$ by $2$ and simplify.

Divide each term in $2 x = 2$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2}$

$y = 2 x + 3$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2}$

$y = 2 x + 3$

Divide $x$ by $1$ .

$x = \frac{2}{2}$

$y = 2 x + 3$

$x = \frac{2}{2}$

$y = 2 x + 3$

$x = \frac{2}{2}$

$y = 2 x + 3$

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

$y = 2 x + 3$

$x = 1$

$y = 2 x + 3$

$x = 1$

$y = 2 x + 3$

$x = 1$

$y = 2 x + 3$

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = 2 x + 3$ with $1$ .

$y = 2 (1) + 3$

$x = 1$

Simplify the right side.

Simplify $2 (1) + 3$ .

Multiply $2$ by $1$ .

$y = 2 + 3$

$x = 1$

Add $2$ and $3$ .

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(1, 5)$

The result can be shown in multiple forms.

Point Form:

$(1, 5)$

Equation Form:

$x = 1, y = 5$

Solve by Substitution y=2x+3 and 2y-2x=8

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