Precalculus Examples

$4 x - y = 3$ , $- 20 x + 5 y = - 15$ , $(3, 9)$

Step 1

Simplify $4 (3) - (9)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $4$ by $3$ .

$12 - (9) = 3$

$- 20 \cdot 3 + 5 (9) = - 15$

Step 1.1.2

Multiply $- 1$ by $9$ .

$12 - 9 = 3$

$- 20 \cdot 3 + 5 (9) = - 15$

$12 - 9 = 3$

$- 20 \cdot 3 + 5 (9) = - 15$

Step 1.2

Subtract $9$ from $12$ .

$3 = 3$

$- 20 \cdot 3 + 5 (9) = - 15$

$3 = 3$

$- 20 \cdot 3 + 5 (9) = - 15$

Step 2

Since $3 = 3$ , the equation will always be true.

Always true

$- 20 \cdot 3 + 5 (9) = - 15$

Step 3

Simplify $- 20 \cdot 3 + 5 (9)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $- 20$ by $3$ .

$- 60 + 5 (9) = - 15$

Always true

Step 3.1.2

Multiply $5$ by $9$ .

$- 60 + 45 = - 15$

Always true

$- 60 + 45 = - 15$

Always true

Step 3.2

Add $- 60$ and $45$ .

$- 15 = - 15$

Always true

$- 15 = - 15$

Always true

Step 4

Since $- 15 = - 15$ , the equation will always be true.

Always true

Step 5

The ordered pair is a solution to the system of equations.

$(3, 9)$ is a solution