Algebra Examples

$3 x - \frac{1}{2} y = - \frac{7}{2}$ $x + 2 y = 1$

Step 1

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

$x = 1 - 2 y$

$3 x - \frac{1}{2} y = - \frac{7}{2}$

Step 2

Replace all occurrences of $x$ with $1 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 x - \frac{1}{2} y = - \frac{7}{2}$ with $1 - 2 y$ .

$3 (1 - 2 y) - \frac{1}{2} y = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$3 \cdot 1 + 3 (- 2 y) - \frac{1}{2} y = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.1.2

Multiply $3$ by $1$ .

$3 + 3 (- 2 y) - \frac{1}{2} y = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $3$ .

$3 - 6 y - \frac{1}{2} y = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.1.4

Combine $y$ and $\frac{1}{2}$ .

$3 - 6 y - \frac{y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

$3 - 6 y - \frac{y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.2

To write $- 6 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 - 6 y \cdot \frac{2}{2} - \frac{y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $- 6 y$ and $\frac{2}{2}$ .

$3 + \frac{- 6 y \cdot 2}{2} - \frac{y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$3 + \frac{- 6 y \cdot 2 - y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

$3 + \frac{- 6 y \cdot 2 - y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

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 $y$ out of $- 6 y \cdot 2 - y$ .

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Step 2.2.1.4.1.1.1

Factor $y$ out of $- 6 y \cdot 2$ .

$3 + \frac{y (- 6 \cdot 2) - y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.4.1.1.2

Factor $y$ out of $- y$ .

$3 + \frac{y (- 6 \cdot 2) + y \cdot - 1}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.4.1.1.3

Factor $y$ out of $y (- 6 \cdot 2) + y \cdot - 1$ .

$3 + \frac{y (- 6 \cdot 2 - 1)}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

$3 + \frac{y (- 6 \cdot 2 - 1)}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.4.1.2

Multiply $- 6$ by $2$ .

$3 + \frac{y (- 12 - 1)}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.4.1.3

Subtract $1$ from $- 12$ .

$3 + \frac{y \cdot - 13}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

$3 + \frac{y \cdot - 13}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.4.2

Move $- 13$ to the left of $y$ .

$3 + \frac{- 13 \cdot y}{2} = - \frac{7}{2}$

$x = 1 - 2 y$

Step 2.2.1.4.3

Move the negative in front of the fraction.