Algebra Examples

$2 x - y = 17$ $x - y = 10$

Step 1

Add $y$ to both sides of the equation.

$x = 10 + y$

$2 x - y = 17$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $2 x - y = 17$ with $10 + y$ .

$2 (10 + y) - y = 17$

$x = 10 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (10 + y) - y$ .

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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.

$2 \cdot 10 + 2 y - y = 17$

$x = 10 + y$

Step 2.2.1.1.2

Multiply $2$ by $10$ .

$20 + 2 y - y = 17$

$x = 10 + y$

$20 + 2 y - y = 17$

$x = 10 + y$

Step 2.2.1.2

Subtract $y$ from $2 y$ .

$20 + y = 17$

$x = 10 + y$

$20 + y = 17$

$x = 10 + y$

$20 + y = 17$

$x = 10 + y$

$20 + y = 17$

$x = 10 + y$

Step 3

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

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Step 3.1

Subtract $20$ from both sides of the equation.

$y = 17 - 20$

$x = 10 + y$

Step 3.2

Subtract $20$ from $17$ .

$y = - 3$

$x = 10 + y$

$y = - 3$

$x = 10 + y$

Step 4

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

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Step 4.1

Replace all occurrences of $y$ in $x = 10 + y$ with $- 3$ .

$x = 10 - 3$

$y = - 3$

Step 4.2

Simplify $x = 10 - 3$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = 10 - 3$

$y = - 3$

$x = 10 - 3$

$y = - 3$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Subtract $3$ from $10$ .

$x = 7$

$y = - 3$

$x = 7$

$y = - 3$

$x = 7$

$y = - 3$

$x = 7$

$y = - 3$

Step 5

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

$(7, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, - 3)$

Equation Form:

$x = 7, y = - 3$

Step 7