Finite Math Examples

$y = 3 x - 5$ , $y = 5 x - 7$

Step 1

Eliminate the equal sides of each equation and combine.

$3 x - 5 = 5 x - 7$

Step 2

Solve $3 x - 5 = 5 x - 7$ for $x$ .

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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

Subtract $5 x$ from both sides of the equation.

$3 x - 5 - 5 x = - 7$

Step 2.1.2

Subtract $5 x$ from $3 x$ .

$- 2 x - 5 = - 7$

Step 2.2

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

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Step 2.2.1

Add $5$ to both sides of the equation.

$- 2 x = - 7 + 5$

Step 2.2.2

Add $- 7$ and $5$ .

$- 2 x = - 2$

Step 2.3

Divide each term in $- 2 x = - 2$ by $- 2$ and simplify.

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Step 2.3.1

Divide each term in $- 2 x = - 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{- 2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 2$ by $- 2$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

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Step 3.1

Substitute $1$ for $x$ .

$y = 5 (1) - 7$

Step 3.2

Simplify $5 (1) - 7$ .

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Step 3.2.1

Multiply $5$ by $1$ .

$y = 5 - 7$

Step 3.2.2

Subtract $7$ from $5$ .

$y = - 2$

Step 4

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

$(1, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, - 2)$

Equation Form:

$x = 1, y = - 2$

Step 6