Algebra Examples

$y = \frac{7}{4} x - 3$ $y = x$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{7}{4} x - 3 = x$

Step 2

Solve $\frac{7}{4} x - 3 = x$ for $x$ .

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Step 2.1

Combine $\frac{7}{4}$ and $x$ .

$\frac{7 x}{4} - 3 = x$

Step 2.2

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

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Step 2.2.1

Subtract $x$ from both sides of the equation.

$\frac{7 x}{4} - 3 - x = 0$

Step 2.2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 x}{4} - x \cdot \frac{4}{4} - 3 = 0$

Step 2.2.3

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

$\frac{7 x}{4} + \frac{- x \cdot 4}{4} - 3 = 0$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{7 x - x \cdot 4}{4} - 3 = 0$

Step 2.2.5

Simplify each term.

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Step 2.2.5.1

Simplify the numerator.

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Step 2.2.5.1.1

Factor $x$ out of $7 x - x \cdot 4$ .

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Step 2.2.5.1.1.1

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 - x \cdot 4}{4} - 3 = 0$

Step 2.2.5.1.1.2

Factor $x$ out of $- x \cdot 4$ .

$\frac{x \cdot 7 + x (- 1 \cdot 4)}{4} - 3 = 0$

Step 2.2.5.1.1.3

Factor $x$ out of $x \cdot 7 + x (- 1 \cdot 4)$ .

$\frac{x (7 - 1 \cdot 4)}{4} - 3 = 0$

Step 2.2.5.1.2

Multiply $- 1$ by $4$ .

$\frac{x (7 - 4)}{4} - 3 = 0$

Step 2.2.5.1.3

Subtract $4$ from $7$ .

$\frac{x \cdot 3}{4} - 3 = 0$

Step 2.2.5.2

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

$\frac{3 x}{4} - 3 = 0$

Step 2.3

Add $3$ to both sides of the equation.

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

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 $x$ .

$y = 4$

Step 3.2

Remove parentheses.

$y = 4$

Step 4

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

$(4, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 4)$

Equation Form:

$x = 4, y = 4$

Step 6