Algebra Examples

$- 4 x + 2 y = 0$ $10 x + 3 y = 8$

Step 1

Solve for $x$ in $- 4 x + 2 y = 0$ .

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Step 1.1

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

$- 4 x = - 2 y$

$10 x + 3 y = 8$

Step 1.2

Divide each term in $- 4 x = - 2 y$ by $- 4$ and simplify.

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Step 1.2.1

Divide each term in $- 4 x = - 2 y$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 2 y}{- 4}$

$10 x + 3 y = 8$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 2 y}{- 4}$

$10 x + 3 y = 8$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2 y}{- 4}$

$10 x + 3 y = 8$

$x = \frac{- 2 y}{- 4}$

$10 x + 3 y = 8$

$x = \frac{- 2 y}{- 4}$

$10 x + 3 y = 8$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Cancel the common factor of $- 2$ and $- 4$ .

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Step 1.2.3.1.1

Factor $- 2$ out of $- 2 y$ .

$x = \frac{- 2 y}{- 4}$

$10 x + 3 y = 8$

Step 1.2.3.1.2

Cancel the common factors.

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Step 1.2.3.1.2.1

Factor $- 2$ out of $- 4$ .

$x = \frac{- 2 y}{- 2 \cdot 2}$

$10 x + 3 y = 8$

Step 1.2.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 y}{- 2 \cdot 2}$

$10 x + 3 y = 8$

Step 1.2.3.1.2.3

Rewrite the expression.

$x = \frac{y}{2}$

$10 x + 3 y = 8$

$x = \frac{y}{2}$

$10 x + 3 y = 8$

$x = \frac{y}{2}$

$10 x + 3 y = 8$

$x = \frac{y}{2}$

$10 x + 3 y = 8$

$x = \frac{y}{2}$

$10 x + 3 y = 8$

$x = \frac{y}{2}$

$10 x + 3 y = 8$

Step 2

Replace all occurrences of $x$ with $\frac{y}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $10 x + 3 y = 8$ with $\frac{y}{2}$ .

$10 (\frac{y}{2}) + 3 y = 8$

$x = \frac{y}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $10 (\frac{y}{2}) + 3 y$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $10$ .

$2 (5) (\frac{y}{2}) + 3 y = 8$

$x = \frac{y}{2}$

Step 2.2.1.1.2

Cancel the common factor.

$2 \cdot (5 (\frac{y}{2})) + 3 y = 8$

$x = \frac{y}{2}$

Step 2.2.1.1.3

Rewrite the expression.

$5 y + 3 y = 8$

$x = \frac{y}{2}$

$5 y + 3 y = 8$

$x = \frac{y}{2}$

Step 2.2.1.2

Add $5 y$ and $3 y$ .

$8 y = 8$

$x = \frac{y}{2}$

$8 y = 8$

$x = \frac{y}{2}$

$8 y = 8$

$x = \frac{y}{2}$

$8 y = 8$

$x = \frac{y}{2}$

Step 3

Divide each term in $8 y = 8$ by $8$ and simplify.

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Step 3.1

Divide each term in $8 y = 8$ by $8$ .

$\frac{8 y}{8} = \frac{8}{8}$

$x = \frac{y}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{8}{8}$

$x = \frac{y}{2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{8}$

$x = \frac{y}{2}$

$y = \frac{8}{8}$

$x = \frac{y}{2}$

$y = \frac{8}{8}$

$x = \frac{y}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $8$ by $8$ .

$y = 1$

$x = \frac{y}{2}$

$y = 1$

$x = \frac{y}{2}$

$y = 1$

$x = \frac{y}{2}$

Step 4

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

$x = \frac{1}{2}$

$y = 1$

Step 5

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

$(\frac{1}{2}, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{1}{2}, 1)$

Equation Form:

$x = \frac{1}{2}, y = 1$

Step 7