Finite Math Examples

$y = x$ , $x = - 3 y$

Step 1

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

$x = - 3 x$

$y = x$

Step 2

Solve for $x$ in $x = - 3 x$ .

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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

Add $3 x$ to both sides of the equation.

$x + 3 x = 0$

$y = x$

Step 2.1.2

Add $x$ and $3 x$ .

$4 x = 0$

$y = x$

$4 x = 0$

$y = x$

Step 2.2

Divide each term in $4 x = 0$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

$y = x$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

$y = x$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{4}$

$y = x$

$x = \frac{0}{4}$

$y = x$

$x = \frac{0}{4}$

$y = x$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $0$ by $4$ .

$x = 0$

$y = x$

$x = 0$

$y = x$

$x = 0$

$y = x$

$x = 0$

$y = x$

Step 3

Replace all occurrences of $x$ with $0$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = x$ with $0$ .

$y = 0$

$x = 0$

Step 3.2

Simplify the left side.

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Step 3.2.1

Remove parentheses.

$y = 0$

$x = 0$

$y = 0$

$x = 0$

$y = 0$

$x = 0$

Step 4

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

$(0, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 0)$

Equation Form:

$x = 0, y = 0$

Step 6