Finite Math Examples

$y = 3 x + 1$ , $y = 2 x - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$3 x + 1 = 2 x - 1$

Step 2

Solve $3 x + 1 = 2 x - 1$ 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 $2 x$ from both sides of the equation.

$3 x + 1 - 2 x = - 1$

Step 2.1.2

Subtract $2 x$ from $3 x$ .

$x + 1 = - 1$

Step 2.2

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

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Step 2.2.1

Subtract $1$ from both sides of the equation.

$x = - 1 - 1$

Step 2.2.2

Subtract $1$ from $- 1$ .

$x = - 2$

Step 3

Evaluate $y$ when $x = - 2$ .

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Step 3.1

Substitute $- 2$ for $x$ .

$y = 2 (- 2) - 1$

Step 3.2

Simplify $2 (- 2) - 1$ .

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Step 3.2.1

Multiply $2$ by $- 2$ .

$y = - 4 - 1$

Step 3.2.2

Subtract $1$ from $- 4$ .

$y = - 5$

Step 4

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

$(- 2, - 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, - 5)$

Equation Form:

$x = - 2, y = - 5$

Step 6