Finite Math Examples

$y = x^{2}$ , $y = 3 x + 4$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} = 3 x + 4$

Step 2

Solve $x^{2} = 3 x + 4$ for $x$ .

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Step 2.1

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

$x^{2} - 3 x = 4$

Step 2.2

Subtract $4$ from both sides of the equation.

$x^{2} - 3 x - 4 = 0$

Step 2.3

Factor $x^{2} - 3 x - 4$ using the AC method.

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Step 2.3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 4$ and whose sum is $- 3$ .

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

Step 2.3.2

Write the factored form using these integers.

$(x - 4) (x + 1) = 0$

Step 2.4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 4 = 0$

$x + 1 = 0 + y = 3 x + 4$

Step 2.5

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 2.5.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.5.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.6

Set $x + 1$ equal to $0$ and solve for $x$ .

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Step 2.6.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 2.6.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.7

The final solution is all the values that make $(x - 4) (x + 1) = 0$ true.

$x = 4, - 1$

Step 3

Evaluate $y$ when $x = 4$ .

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Step 3.1

Substitute $4$ for $x$ .

$y = 3 (4) + 4$

Step 3.2

Simplify $3 (4) + 4$ .

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Step 3.2.1

Multiply $3$ by $4$ .

$y = 12 + 4$

Step 3.2.2

Add $12$ and $4$ .

$y = 16$

Step 4

Evaluate $y$ when $x = - 1$ .

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Step 4.1

Substitute $- 1$ for $x$ .

$y = 3 (- 1) + 4$

Step 4.2

Simplify $3 (- 1) + 4$ .

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Step 4.2.1

Multiply $3$ by $- 1$ .

$y = - 3 + 4$

Step 4.2.2

Add $- 3$ and $4$ .

$y = 1$

Step 5

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

$(4, 16)$

$(- 1, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 16), (- 1, 1)$

Equation Form:

$x = 4, y = 16$

$x = - 1, y = 1$

Step 7