Algebra Examples

$y = - \frac{3}{5} x - 1$ $y = - \frac{4}{5} x$

Step 1

Eliminate the equal sides of each equation and combine.

$- \frac{3}{5} x - 1 = - \frac{4}{5} x$

Step 2

Solve $- \frac{3}{5} x - 1 = - \frac{4}{5} x$ for $x$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Combine $x$ and $\frac{3}{5}$ .

$- \frac{x \cdot 3}{5} - 1 = - \frac{4}{5} x$

Step 2.1.2

Move $3$ to the left of $x$ .

$- \frac{3 x}{5} - 1 = - \frac{4}{5} x$

Step 2.2

Simplify $- \frac{4}{5} x$ .

Tap for more steps...

Step 2.2.1

Combine $x$ and $\frac{4}{5}$ .

$- \frac{3 x}{5} - 1 = - \frac{x \cdot 4}{5}$

Step 2.2.2

Move $4$ to the left of $x$ .

$- \frac{3 x}{5} - 1 = - \frac{4 x}{5}$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Add $\frac{4 x}{5}$ to both sides of the equation.

$- \frac{3 x}{5} - 1 + \frac{4 x}{5} = 0$

Step 2.3.2

Combine the numerators over the common denominator.

$- 1 + \frac{- 3 x + 4 x}{5} = 0$

Step 2.3.3

Add $- 3 x$ and $4 x$ .

$- 1 + \frac{x}{5} = 0$

Step 2.4

Add $1$ to both sides of the equation.

$\frac{x}{5} = 1$

Step 2.5

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot 1$

Step 2.6

Simplify both sides of the equation.

Tap for more steps...

Step 2.6.1

Simplify the left side.

Tap for more steps...

Step 2.6.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.6.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot 1$

Step 2.6.1.1.2

Rewrite the expression.

$x = 5 \cdot 1$

Step 2.6.2

Simplify the right side.

Tap for more steps...

Step 2.6.2.1

Multiply $5$ by $1$ .

$x = 5$

Step 3

Evaluate $y$ when $x = 5$ .

Tap for more steps...

Step 3.1

Substitute $5$ for $x$ .

$y = - \frac{4}{5} \cdot 5$

Step 3.2

Substitute $5$ for $x$ in $y = - \frac{4}{5} \cdot 5$ and solve for $y$ .

Tap for more steps...

Step 3.2.1

Remove parentheses.

$y = - \frac{4}{5} \cdot 5$

Step 3.2.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.2.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$y = \frac{- 4}{5} \cdot 5$

Step 3.2.2.2

Cancel the common factor.

$y = \frac{- 4}{5} \cdot 5$

Step 3.2.2.3

Rewrite the expression.

$y = - 4$

Step 4

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

$(5, - 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, - 4)$

Equation Form:

$x = 5, y = - 4$

Step 6