Algebra Examples

$\frac{1}{3} x - y = 3$ $2 x + y = 25$

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 25 - 2 x$

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

Step 2

Replace all occurrences of $y$ with $25 - 2 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $\frac{1}{3} x - y = 3$ with $25 - 2 x$ .

$\frac{1}{3} x - (25 - 2 x) = 3$

$y = 25 - 2 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{1}{3} x - (25 - 2 x)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} - (25 - 2 x) = 3$

$y = 25 - 2 x$

Step 2.2.1.1.2

Apply the distributive property.

$\frac{x}{3} - 1 \cdot 25 - (- 2 x) = 3$

$y = 25 - 2 x$

Step 2.2.1.1.3

Multiply $- 1$ by $25$ .

$\frac{x}{3} - 25 - (- 2 x) = 3$

$y = 25 - 2 x$

Step 2.2.1.1.4

Multiply $- 2$ by $- 1$ .

$\frac{x}{3} - 25 + 2 x = 3$

$y = 25 - 2 x$

$\frac{x}{3} - 25 + 2 x = 3$

$y = 25 - 2 x$

Step 2.2.1.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} + 2 x \cdot \frac{3}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $2 x$ and $\frac{3}{3}$ .

$\frac{x}{3} + \frac{2 x \cdot 3}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$\frac{x + 2 x \cdot 3}{3} - 25 = 3$

$y = 25 - 2 x$

$\frac{x + 2 x \cdot 3}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.4

Simplify each term.

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Step 2.2.1.4.1

Simplify the numerator.

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Step 2.2.1.4.1.1

Factor $x$ out of $x + 2 x \cdot 3$ .

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Step 2.2.1.4.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x + 2 x \cdot 3}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.4.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 + 2 x \cdot 3}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.4.1.1.3

Factor $x$ out of $2 x \cdot 3$ .

$\frac{x \cdot 1 + x (2 \cdot 3)}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.4.1.1.4

Factor $x$ out of $x \cdot 1 + x (2 \cdot 3)$ .

$\frac{x (1 + 2 \cdot 3)}{3} - 25 = 3$

$y = 25 - 2 x$

$\frac{x (1 + 2 \cdot 3)}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.4.1.2

Multiply $2$ by $3$ .

$\frac{x (1 + 6)}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.4.1.3

Add $1$ and $6$ .

$\frac{x \cdot 7}{3} - 25 = 3$

$y = 25 - 2 x$

$\frac{x \cdot 7}{3} - 25 = 3$

$y = 25 - 2 x$

Step 2.2.1.4.2

Move $7$ to the left of $x$ .

$\frac{7 x}{3} - 25 = 3$

$y = 25 - 2 x$

$\frac{7 x}{3} - 25 = 3$

$y = 25 - 2 x$

$\frac{7 x}{3} - 25 = 3$

$y = 25 - 2 x$

$\frac{7 x}{3} - 25 = 3$

$y = 25 - 2 x$

$\frac{7 x}{3} - 25 = 3$

$y = 25 - 2 x$

Step 3

Solve for $x$ in $\frac{7 x}{3} - 25 = 3$ .

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Step 3.1

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

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Step 3.1.1

Add $25$ to both sides of the equation.

$\frac{7 x}{3} = 3 + 25$

$y = 25 - 2 x$

Step 3.1.2

Add $3$ and $25$ .

$\frac{7 x}{3} = 28$

$y = 25 - 2 x$

$\frac{7 x}{3} = 28$

$y = 25 - 2 x$

Step 3.2

Multiply both sides of the equation by $\frac{3}{7}$ .

$\frac{3}{7} \cdot \frac{7 x}{3} = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{3}{7} \cdot \frac{7 x}{3}$ .

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Step 3.3.1.1.1

Cancel the common factor of $3$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{3}{7} \cdot \frac{7 x}{3} = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{7} \cdot (7 x) = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

$\frac{1}{7} \cdot (7 x) = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

Step 3.3.1.1.2

Cancel the common factor of $7$ .

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Step 3.3.1.1.2.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} \cdot (7 (x)) = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{7} \cdot (7 x) = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

$x = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

$x = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

$x = \frac{3}{7} \cdot 28$

$y = 25 - 2 x$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{3}{7} \cdot 28$ .

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Step 3.3.2.1.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1.1

Factor $7$ out of $28$ .

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

$y = 25 - 2 x$

Step 3.3.2.1.1.2

Cancel the common factor.

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

$y = 25 - 2 x$

Step 3.3.2.1.1.3

Rewrite the expression.

$x = 3 \cdot 4$

$y = 25 - 2 x$

$x = 3 \cdot 4$

$y = 25 - 2 x$

Step 3.3.2.1.2

Multiply $3$ by $4$ .

$x = 12$

$y = 25 - 2 x$

$x = 12$

$y = 25 - 2 x$

$x = 12$

$y = 25 - 2 x$

$x = 12$

$y = 25 - 2 x$

$x = 12$

$y = 25 - 2 x$

Step 4

Replace all occurrences of $x$ with $12$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = 25 - 2 x$ with $12$ .

$y = 25 - 2 \cdot 12$

$x = 12$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $25 - 2 \cdot 12$ .

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Step 4.2.1.1

Multiply $- 2$ by $12$ .

$y = 25 - 24$

$x = 12$

Step 4.2.1.2

Subtract $24$ from $25$ .

$y = 1$

$x = 12$

$y = 1$

$x = 12$

$y = 1$

$x = 12$

$y = 1$

$x = 12$

Step 5

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

$(12, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(12, 1)$

Equation Form:

$x = 12, y = 1$

Step 7