Algebra Examples

$y = 2 x - 10$ $2 y = x - 8$

Step 1

Replace all occurrences of $y$ with $2 x - 10$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $2 y = x - 8$ with $2 x - 10$ .

$2 (2 x - 10) = x - 8$

$y = 2 x - 10$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $2 (2 x - 10)$ .

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Step 1.2.1.1

Apply the distributive property.

$2 (2 x) + 2 \cdot - 10 = x - 8$

$y = 2 x - 10$

Step 1.2.1.2

Multiply.

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Step 1.2.1.2.1

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 10 = x - 8$

$y = 2 x - 10$

Step 1.2.1.2.2

Multiply $2$ by $- 10$ .

$4 x - 20 = x - 8$

$y = 2 x - 10$

$4 x - 20 = x - 8$

$y = 2 x - 10$

$4 x - 20 = x - 8$

$y = 2 x - 10$

$4 x - 20 = x - 8$

$y = 2 x - 10$

$4 x - 20 = x - 8$

$y = 2 x - 10$

Step 2

Solve for $x$ in $4 x - 20 = x - 8$ .

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Step 2.1

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

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Step 2.1.1

Subtract $x$ from both sides of the equation.

$4 x - 20 - x = - 8$

$y = 2 x - 10$

Step 2.1.2

Subtract $x$ from $4 x$ .

$3 x - 20 = - 8$

$y = 2 x - 10$

$3 x - 20 = - 8$

$y = 2 x - 10$

Step 2.2

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

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Step 2.2.1

Add $20$ to both sides of the equation.

$3 x = - 8 + 20$

$y = 2 x - 10$

Step 2.2.2

Add $- 8$ and $20$ .

$3 x = 12$

$y = 2 x - 10$

$3 x = 12$

$y = 2 x - 10$

Step 2.3

Divide each term in $3 x = 12$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 x = 12$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3}$

$y = 2 x - 10$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3}$

$y = 2 x - 10$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{3}$

$y = 2 x - 10$

$x = \frac{12}{3}$

$y = 2 x - 10$

$x = \frac{12}{3}$

$y = 2 x - 10$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $12$ by $3$ .

$x = 4$

$y = 2 x - 10$

$x = 4$

$y = 2 x - 10$

$x = 4$

$y = 2 x - 10$

$x = 4$

$y = 2 x - 10$

Step 3

Replace all occurrences of $x$ with $4$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = 2 x - 10$ with $4$ .

$y = 2 (4) - 10$

$x = 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $2 (4) - 10$ .

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Step 3.2.1.1

Multiply $2$ by $4$ .

$y = 8 - 10$

$x = 4$

Step 3.2.1.2

Subtract $10$ from $8$ .

$y = - 2$

$x = 4$

$y = - 2$

$x = 4$

$y = - 2$

$x = 4$

$y = - 2$

$x = 4$

Step 4

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

$(4, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, - 2)$

Equation Form:

$x = 4, y = - 2$

Step 6