Algebra Examples

Solve the system of equations $y = 2 x + 3$ and $2 y + 2 x = - 6$ using the Substitution Method.

Step 1

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

Tap for more steps...

Step 1.1

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

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

$y = 2 x + 3$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

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

Tap for more steps...

Step 1.2.1.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1.1

Apply the distributive property.

$2 (2 x) + 2 \cdot 3 + 2 x = - 6$

$y = 2 x + 3$

Step 1.2.1.1.2

Multiply $2$ by $2$ .

$4 x + 2 \cdot 3 + 2 x = - 6$

$y = 2 x + 3$

Step 1.2.1.1.3

Multiply $2$ by $3$ .

$4 x + 6 + 2 x = - 6$

$y = 2 x + 3$

$4 x + 6 + 2 x = - 6$

$y = 2 x + 3$

Step 1.2.1.2

Add $4 x$ and $2 x$ .

$6 x + 6 = - 6$

$y = 2 x + 3$

$6 x + 6 = - 6$

$y = 2 x + 3$

$6 x + 6 = - 6$

$y = 2 x + 3$

$6 x + 6 = - 6$

$y = 2 x + 3$

Step 2

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

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Subtract $6$ from both sides of the equation.

$6 x = - 6 - 6$

$y = 2 x + 3$

Step 2.1.2

Subtract $6$ from $- 6$ .

$6 x = - 12$

$y = 2 x + 3$

$6 x = - 12$

$y = 2 x + 3$

Step 2.2

Divide each term in $6 x = - 12$ by $6$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $6 x = - 12$ by $6$ .

$\frac{6 x}{6} = \frac{- 12}{6}$

$y = 2 x + 3$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 12}{6}$

$y = 2 x + 3$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{6}$

$y = 2 x + 3$

$x = \frac{- 12}{6}$

$y = 2 x + 3$

$x = \frac{- 12}{6}$

$y = 2 x + 3$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $- 12$ by $6$ .

$x = - 2$

$y = 2 x + 3$

$x = - 2$

$y = 2 x + 3$

$x = - 2$

$y = 2 x + 3$

$x = - 2$

$y = 2 x + 3$

Step 3

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

Tap for more steps...

Step 3.1

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

$y = 2 (- 2) + 3$

$x = - 2$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $2 (- 2) + 3$ .

Tap for more steps...

Step 3.2.1.1

Multiply $2$ by $- 2$ .

$y = - 4 + 3$

$x = - 2$

Step 3.2.1.2

Add $- 4$ and $3$ .

$y = - 1$

$x = - 2$

$y = - 1$

$x = - 2$

$y = - 1$

$x = - 2$

$y = - 1$

$x = - 2$

Step 4

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

$(- 2, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, - 1)$

Equation Form:

$x = - 2, y = - 1$

Step 6