Algebra Examples

$2 x - y = 8$ $y = x - 3$

Step 1

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

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Step 1.1

Replace all occurrences of $y$ in $2 x - y = 8$ with $x - 3$ .

$2 x - (x - 3) = 8$

$y = x - 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $2 x - (x - 3)$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$2 x - x + 3 = 8$

$y = x - 3$

Step 1.2.1.1.2

Multiply $- 1$ by $- 3$ .

$2 x - x + 3 = 8$

$y = x - 3$

$2 x - x + 3 = 8$

$y = x - 3$

Step 1.2.1.2

Subtract $x$ from $2 x$ .

$x + 3 = 8$

$y = x - 3$

$x + 3 = 8$

$y = x - 3$

$x + 3 = 8$

$y = x - 3$

$x + 3 = 8$

$y = x - 3$

Step 2

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

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Step 2.1

Subtract $3$ from both sides of the equation.

$x = 8 - 3$

$y = x - 3$

Step 2.2

Subtract $3$ from $8$ .

$x = 5$

$y = x - 3$

$x = 5$

$y = x - 3$

Step 3

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

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Step 3.1

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

$y = (5) - 3$

$x = 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Subtract $3$ from $5$ .

$y = 2$

$x = 5$

$y = 2$

$x = 5$

$y = 2$

$x = 5$

Step 4

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

$(5, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, 2)$

Equation Form:

$x = 5, y = 2$

Step 6