Algebra Examples

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

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

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

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Step 2.1

Rewrite the equation as $\frac{3}{4} x - 4 = - 1$ .

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

Step 2.2

Combine $\frac{3}{4}$ and $x$ .

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

Step 2.3

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

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Step 2.3.1

Add $4$ to both sides of the equation.

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

Step 2.3.2

Add $- 1$ and $4$ .

$\frac{3 x}{4} = 3$

Step 2.4

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot 3$

Step 2.5

Simplify both sides of the equation.

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Step 2.5.1

Simplify the left side.

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Step 2.5.1.1

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

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Step 2.5.1.1.1

Cancel the common factor of $4$ .

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Step 2.5.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot 3$

Step 2.5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot 3$

Step 2.5.1.1.2

Cancel the common factor of $3$ .

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Step 2.5.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot 3$

Step 2.5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot 3$

Step 2.5.1.1.2.3

Rewrite the expression.

$x = \frac{4}{3} \cdot 3$

Step 2.5.2

Simplify the right side.

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Step 2.5.2.1

Cancel the common factor of $3$ .

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Step 2.5.2.1.1

Cancel the common factor.

$x = \frac{4}{3} \cdot 3$

Step 2.5.2.1.2

Rewrite the expression.

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

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Step 3.1

Substitute $4$ for $x$ .

$y = \frac{3}{4} \cdot (4) - 4$

Step 3.2

Substitute $4$ for $x$ in $y = \frac{3}{4} \cdot (4) - 4$ and solve for $y$ .

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Step 3.2.1

Multiply $\frac{3}{4}$ by $4$ .

$y = \frac{3}{4} \cdot 4 - 4$

Step 3.2.2

Simplify $\frac{3}{4} \cdot 4 - 4$ .

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$y = \frac{3}{4} \cdot 4 - 4$

Step 3.2.2.1.2

Rewrite the expression.

$y = 3 - 4$

Step 3.2.2.2

Subtract $4$ from $3$ .

$y = - 1$

Step 4

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

$(4, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, - 1)$

Equation Form:

$x = 4, y = - 1$

Step 6