Solve by Substitution y=2x+3 , 5x-y=-3

$y = 2 x + 3$ , $5 x - y = - 3$

Step 1

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

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

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

$y = 2 x + 3$

Simplify the left side.

Simplify $5 x - (2 x + 3)$ .

Simplify each term.

Apply the distributive property.

$5 x - (2 x) - 1 \cdot 3 = - 3$

$y = 2 x + 3$

Multiply $2$ by $- 1$ .

$5 x - 2 x - 1 \cdot 3 = - 3$

$y = 2 x + 3$

Multiply $- 1$ by $3$ .

$5 x - 2 x - 3 = - 3$

$y = 2 x + 3$

$5 x - 2 x - 3 = - 3$

$y = 2 x + 3$

Subtract $2 x$ from $5 x$ .

$3 x - 3 = - 3$

$y = 2 x + 3$

$3 x - 3 = - 3$

$y = 2 x + 3$

$3 x - 3 = - 3$

$y = 2 x + 3$

$3 x - 3 = - 3$

$y = 2 x + 3$

Step 2

Solve for $x$ in $3 x - 3 = - 3$ .

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

Add $3$ to both sides of the equation.

$3 x = - 3 + 3$

$y = 2 x + 3$

Add $- 3$ and $3$ .

$3 x = 0$

$y = 2 x + 3$

$3 x = 0$

$y = 2 x + 3$

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

$y = 2 x + 3$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

$y = 2 x + 3$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

$y = 2 x + 3$

$x = \frac{0}{3}$

$y = 2 x + 3$

$x = \frac{0}{3}$

$y = 2 x + 3$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$

$y = 2 x + 3$

$x = 0$

$y = 2 x + 3$

$x = 0$

$y = 2 x + 3$

$x = 0$

$y = 2 x + 3$

Step 3

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $y = 2 x + 3$ with $0$ .

$y = 2 (0) + 3$

$x = 0$

Simplify the right side.

Simplify $2 (0) + 3$ .

Multiply $2$ by $0$ .

$y = 0 + 3$

$x = 0$

Add $0$ and $3$ .

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

Step 4

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

$(0, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 3)$

Equation Form:

$x = 0, y = 3$

Step 6

Solve by Substitution y=2x+3 , 5x-y=-3

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