Algebra Examples

$y = 4 x$ and $x + y = 5$

Step 1

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

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Step 1.1

Replace all occurrences of $y$ in $x + y = 5$ with $4 x$ .

$x + 4 x = 5$

$y = 4 x$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $x + 4 x$ .

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Step 1.2.1.1

Remove parentheses.

$x + 4 x = 5$

$y = 4 x$

Step 1.2.1.2

Add $x$ and $4 x$ .

$5 x = 5$

$y = 4 x$

$5 x = 5$

$y = 4 x$

$5 x = 5$

$y = 4 x$

$5 x = 5$

$y = 4 x$

Step 2

Divide each term in $5 x = 5$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x = 5$ by $5$ .

$\frac{5 x}{5} = \frac{5}{5}$

$y = 4 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{5}{5}$

$y = 4 x$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{5}$

$y = 4 x$

$x = \frac{5}{5}$

$y = 4 x$

$x = \frac{5}{5}$

$y = 4 x$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $5$ by $5$ .

$x = 1$

$y = 4 x$

$x = 1$

$y = 4 x$

$x = 1$

$y = 4 x$

Step 3

Replace all occurrences of $x$ with $1$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = 4 x$ with $1$ .

$y = 4 (1)$

$x = 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $4$ by $1$ .

$y = 4$

$x = 1$

$y = 4$

$x = 1$

$y = 4$

$x = 1$

Step 4

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

$(1, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 4)$

Equation Form:

$x = 1, y = 4$

Step 6