Finite Math Examples

$y = 20$ , $3 x + y = 5$

Step 1

Replace all occurrences of $y$ with $20$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $3 x + y = 5$ with $20$ .

$3 x + 20 = 5$

$y = 20$

Step 1.2

Simplify the left side.

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Step 1.2.1

Remove parentheses.

$3 x + 20 = 5$

$y = 20$

$3 x + 20 = 5$

$y = 20$

$3 x + 20 = 5$

$y = 20$

Step 2

Solve for $x$ in $3 x + 20 = 5$ .

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Step 2.1

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

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Step 2.1.1

Subtract $20$ from both sides of the equation.

$3 x = 5 - 20$

$y = 20$

Step 2.1.2

Subtract $20$ from $5$ .

$3 x = - 15$

$y = 20$

$3 x = - 15$

$y = 20$

Step 2.2

Divide each term in $3 x = - 15$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x = - 15$ by $3$ .

$\frac{3 x}{3} = \frac{- 15}{3}$

$y = 20$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 15}{3}$

$y = 20$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 15}{3}$

$y = 20$

$x = \frac{- 15}{3}$

$y = 20$

$x = \frac{- 15}{3}$

$y = 20$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 15$ by $3$ .

$x = - 5$

$y = 20$

$x = - 5$

$y = 20$

$x = - 5$

$y = 20$

$x = - 5$

$y = 20$

Step 3

Solve the system of equations.

$x = - 5 y = 20$

Step 4

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

$(- 5, 20)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 5, 20)$

Equation Form:

$x = - 5, y = 20$

Step 6