Algebra Examples

$y = x$ $- 2 x - 5 y = 35$

Step 1

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

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Step 1.1

Replace all occurrences of $y$ in $- 2 x - 5 y = 35$ with $x$ .

$- 2 x - 5 x = 35$

$y = x$

Step 1.2

Simplify the left side.

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Step 1.2.1

Subtract $5 x$ from $- 2 x$ .

$- 7 x = 35$

$y = x$

$- 7 x = 35$

$y = x$

$- 7 x = 35$

$y = x$

Step 2

Divide each term in $- 7 x = 35$ by $- 7$ and simplify.

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Step 2.1

Divide each term in $- 7 x = 35$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{35}{- 7}$

$y = x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{35}{- 7}$

$y = x$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{35}{- 7}$

$y = x$

$x = \frac{35}{- 7}$

$y = x$

$x = \frac{35}{- 7}$

$y = x$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $35$ by $- 7$ .

$x = - 5$

$y = x$

$x = - 5$

$y = x$

$x = - 5$

$y = x$

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 $y = x$ with $- 5$ .

$y = - 5$

$x = - 5$

Step 3.2

Simplify the left side.

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Step 3.2.1

Remove parentheses.

$y = - 5$

$x = - 5$

$y = - 5$

$x = - 5$

$y = - 5$

$x = - 5$

Step 4

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

$(- 5, - 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 5, - 5)$

Equation Form:

$x = - 5, y = - 5$

Step 6