Algebra Examples

$2 x + 3 y = - 4$ , $2 x - y = 7$

Step 1

Solve for $x$ in $2 x + 3 y = - 4$ .

Tap for more steps...

Step 1.1

Subtract $3 y$ from both sides of the equation.

$2 x = - 4 - 3 y$

$2 x - y = 7$

Step 1.2

Divide each term in $2 x = - 4 - 3 y$ by $2$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $2 x = - 4 - 3 y$ by $2$ .

$\frac{2 x}{2} = \frac{- 4}{2} + \frac{- 3 y}{2}$

$2 x - y = 7$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2} + \frac{- 3 y}{2}$

$2 x - y = 7$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{2} + \frac{- 3 y}{2}$

$2 x - y = 7$

$x = \frac{- 4}{2} + \frac{- 3 y}{2}$

$2 x - y = 7$

$x = \frac{- 4}{2} + \frac{- 3 y}{2}$

$2 x - y = 7$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Divide $- 4$ by $2$ .

$x = - 2 + \frac{- 3 y}{2}$

$2 x - y = 7$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = - 2 - \frac{3 y}{2}$

$2 x - y = 7$

$x = - 2 - \frac{3 y}{2}$

$2 x - y = 7$

$x = - 2 - \frac{3 y}{2}$

$2 x - y = 7$

$x = - 2 - \frac{3 y}{2}$

$2 x - y = 7$

$x = - 2 - \frac{3 y}{2}$

$2 x - y = 7$

Step 2

Replace all occurrences of $x$ with $- 2 - \frac{3 y}{2}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $2 x - y = 7$ with $- 2 - \frac{3 y}{2}$ .

$2 (- 2 - \frac{3 y}{2}) - y = 7$

$x = - 2 - \frac{3 y}{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $2 (- 2 - \frac{3 y}{2}) - y$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$2 \cdot - 2 + 2 (- \frac{3 y}{2}) - y = 7$

$x = - 2 - \frac{3 y}{2}$

Step 2.2.1.1.2

Multiply $2$ by $- 2$ .

$- 4 + 2 (- \frac{3 y}{2}) - y = 7$

$x = - 2 - \frac{3 y}{2}$

Step 2.2.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.3.1

Move the leading negative in $- \frac{3 y}{2}$ into the numerator.

$- 4 + 2 (\frac{- 3 y}{2}) - y = 7$

$x = - 2 - \frac{3 y}{2}$

Step 2.2.1.1.3.2

Cancel the common factor.

$- 4 + 2 (\frac{- 3 y}{2}) - y = 7$

$x = - 2 - \frac{3 y}{2}$

Step 2.2.1.1.3.3

Rewrite the expression.

$- 4 - 3 y - y = 7$

$x = - 2 - \frac{3 y}{2}$

$- 4 - 3 y - y = 7$

$x = - 2 - \frac{3 y}{2}$

$- 4 - 3 y - y = 7$

$x = - 2 - \frac{3 y}{2}$

Step 2.2.1.2

Subtract $y$ from $- 3 y$ .

$- 4 - 4 y = 7$

$x = - 2 - \frac{3 y}{2}$

$- 4 - 4 y = 7$

$x = - 2 - \frac{3 y}{2}$

$- 4 - 4 y = 7$

$x = - 2 - \frac{3 y}{2}$

$- 4 - 4 y = 7$

$x = - 2 - \frac{3 y}{2}$

Step 3

Solve for $y$ in $- 4 - 4 y = 7$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $4$ to both sides of the equation.

$- 4 y = 7 + 4$

$x = - 2 - \frac{3 y}{2}$

Step 3.1.2

Add $7$ and $4$ .

$- 4 y = 11$

$x = - 2 - \frac{3 y}{2}$

$- 4 y = 11$

$x = - 2 - \frac{3 y}{2}$

Step 3.2

Divide each term in $- 4 y = 11$ by $- 4$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 4 y = 11$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{11}{- 4}$

$x = - 2 - \frac{3 y}{2}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{11}{- 4}$

$x = - 2 - \frac{3 y}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{11}{- 4}$

$x = - 2 - \frac{3 y}{2}$

$y = \frac{11}{- 4}$

$x = - 2 - \frac{3 y}{2}$

$y = \frac{11}{- 4}$

$x = - 2 - \frac{3 y}{2}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Move the negative in front of the fraction.

$y = - \frac{11}{4}$

$x = - 2 - \frac{3 y}{2}$

$y = - \frac{11}{4}$

$x = - 2 - \frac{3 y}{2}$

$y = - \frac{11}{4}$

$x = - 2 - \frac{3 y}{2}$

$y = - \frac{11}{4}$

$x = - 2 - \frac{3 y}{2}$

Step 4

Replace all occurrences of $y$ with $- \frac{11}{4}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $x = - 2 - \frac{3 y}{2}$ with $- \frac{11}{4}$ .

$x = - 2 - \frac{3 (- \frac{11}{4})}{2}$

$y = - \frac{11}{4}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- 2 - \frac{3 (- \frac{11}{4})}{2}$ .

Tap for more steps...

Step 4.2.1.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1.1

Simplify the numerator.

Tap for more steps...

Step 4.2.1.1.1.1

Multiply $- 1$ by $3$ .

$x = - 2 - \frac{- 3 (\frac{11}{4})}{2}$

$y = - \frac{11}{4}$

Step 4.2.1.1.1.2

Combine $- 3$ and $\frac{11}{4}$ .

$x = - 2 - \frac{\frac{- 3 \cdot 11}{4}}{2}$

$y = - \frac{11}{4}$

$x = - 2 - \frac{\frac{- 3 \cdot 11}{4}}{2}$

$y = - \frac{11}{4}$

Step 4.2.1.1.2

Multiply $- 3$ by $11$ .

$x = - 2 - \frac{\frac{- 33}{4}}{2}$

$y = - \frac{11}{4}$

Step 4.2.1.1.3

Move the negative in front of the fraction.

$x = - 2 - \frac{- \frac{33}{4}}{2}$

$y = - \frac{11}{4}$

Step 4.2.1.1.4

Multiply the numerator by the reciprocal of the denominator.

$x = - 2 - (- \frac{33}{4} \cdot \frac{1}{2})$

$y = - \frac{11}{4}$

Step 4.2.1.1.5

Multiply $- \frac{33}{4} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 4.2.1.1.5.1

Multiply $\frac{1}{2}$ by $\frac{33}{4}$ .

$x = - 2 + \frac{33}{2 \cdot 4}$

$y = - \frac{11}{4}$

Step 4.2.1.1.5.2

Multiply $2$ by $4$ .

$x = - 2 + \frac{33}{8}$

$y = - \frac{11}{4}$

$x = - 2 + \frac{33}{8}$

$y = - \frac{11}{4}$

Step 4.2.1.1.6

Multiply $- - \frac{33}{8}$ .

Tap for more steps...

Step 4.2.1.1.6.1

Multiply $- 1$ by $- 1$ .

$x = - 2 + 1 (\frac{33}{8})$

$y = - \frac{11}{4}$

Step 4.2.1.1.6.2

Multiply $\frac{33}{8}$ by $1$ .

$x = - 2 + \frac{33}{8}$

$y = - \frac{11}{4}$

$x = - 2 + \frac{33}{8}$

$y = - \frac{11}{4}$

$x = - 2 + \frac{33}{8}$

$y = - \frac{11}{4}$

Step 4.2.1.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x = - 2 \cdot \frac{8}{8} + \frac{33}{8}$

$y = - \frac{11}{4}$

Step 4.2.1.3

Combine $- 2$ and $\frac{8}{8}$ .

$x = \frac{- 2 \cdot 8}{8} + \frac{33}{8}$

$y = - \frac{11}{4}$

Step 4.2.1.4

Combine the numerators over the common denominator.

$x = \frac{- 2 \cdot 8 + 33}{8}$

$y = - \frac{11}{4}$

Step 4.2.1.5

Simplify the numerator.

Tap for more steps...

Step 4.2.1.5.1

Multiply $- 2$ by $8$ .

$x = \frac{- 16 + 33}{8}$

$y = - \frac{11}{4}$

Step 4.2.1.5.2

Add $- 16$ and $33$ .

$x = \frac{17}{8}$

$y = - \frac{11}{4}$

$x = \frac{17}{8}$

$y = - \frac{11}{4}$

$x = \frac{17}{8}$

$y = - \frac{11}{4}$

$x = \frac{17}{8}$

$y = - \frac{11}{4}$

$x = \frac{17}{8}$

$y = - \frac{11}{4}$

Step 5

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

$(\frac{17}{8}, - \frac{11}{4})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{17}{8}, - \frac{11}{4})$

Equation Form:

$x = \frac{17}{8}, y = - \frac{11}{4}$

Step 7