Algebra Examples

$2 y = 6 x + 10$ $3 x - y = 5$

Step 1

Divide each term in $2 y = 6 x + 10$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 y = 6 x + 10$ by $2$ .

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{10}{2}$

$3 x - y = 5$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{10}{2}$

$3 x - y = 5$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{2} + \frac{10}{2}$

$3 x - y = 5$

$y = \frac{6 x}{2} + \frac{10}{2}$

$3 x - y = 5$

$y = \frac{6 x}{2} + \frac{10}{2}$

$3 x - y = 5$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $6$ and $2$ .

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Step 1.3.1.1.1

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x)}{2} + \frac{10}{2}$

$3 x - y = 5$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (3 x)}{2 (1)} + \frac{10}{2}$

$3 x - y = 5$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (3 x)}{2 \cdot 1} + \frac{10}{2}$

$3 x - y = 5$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{3 x}{1} + \frac{10}{2}$

$3 x - y = 5$

Step 1.3.1.1.2.4

Divide $3 x$ by $1$ .

$y = 3 x + \frac{10}{2}$

$3 x - y = 5$

$y = 3 x + \frac{10}{2}$

$3 x - y = 5$

$y = 3 x + \frac{10}{2}$

$3 x - y = 5$

Step 1.3.1.2

Divide $10$ by $2$ .

$y = 3 x + 5$

$3 x - y = 5$

$y = 3 x + 5$

$3 x - y = 5$

$y = 3 x + 5$

$3 x - y = 5$

$y = 3 x + 5$

$3 x - y = 5$

Step 2

Replace all occurrences of $y$ with $3 x + 5$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 x - y = 5$ with $3 x + 5$ .

$3 x - (3 x + 5) = 5$

$y = 3 x + 5$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 x - (3 x + 5)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$3 x - (3 x) - 1 \cdot 5 = 5$

$y = 3 x + 5$

Step 2.2.1.1.2

Multiply $3$ by $- 1$ .

$3 x - 3 x - 1 \cdot 5 = 5$

$y = 3 x + 5$

Step 2.2.1.1.3

Multiply $- 1$ by $5$ .

$3 x - 3 x - 5 = 5$

$y = 3 x + 5$

$3 x - 3 x - 5 = 5$

$y = 3 x + 5$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $3 x$ from $3 x$ .

$0 - 5 = 5$

$y = 3 x + 5$

Step 2.2.1.2.2

Subtract $5$ from $0$ .

$- 5 = 5$

$y = 3 x + 5$

$- 5 = 5$

$y = 3 x + 5$

$- 5 = 5$

$y = 3 x + 5$

$- 5 = 5$

$y = 3 x + 5$

$- 5 = 5$

$y = 3 x + 5$

Step 3

Since $- 5 = 5$ is not true, there is no solution.

No solution

Step 4