Finite Math Examples

$y = - 1 x + 4$ , $y = 3 x$

Step 1

Eliminate the equal sides of each equation and combine.

$- 1 x + 4 = 3 x$

Step 2

Solve $- 1 x + 4 = 3 x$ for $x$ .

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Step 2.1

Rewrite $- 1 x$ as $- x$ .

$- x + 4 = 3 x$

Step 2.2

Move all terms containing $x$ to the left side of the equation.

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Step 2.2.1

Subtract $3 x$ from both sides of the equation.

$- x + 4 - 3 x = 0$

Step 2.2.2

Subtract $3 x$ from $- x$ .

$- 4 x + 4 = 0$

Step 2.3

Subtract $4$ from both sides of the equation.

$- 4 x = - 4$

Step 2.4

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

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Step 2.4.1

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

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

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 4$ .

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Step 2.4.2.1.1

Cancel the common factor.

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

Step 2.4.2.1.2

Divide $x$ by $1$ .

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

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 4$ by $- 4$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

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Step 3.1

Substitute $1$ for $x$ .

$y = 3 (1)$

Step 3.2

Multiply $3$ by $1$ .

$y = 3$

Step 4

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

$(1, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 6