Precalculus Examples

$3 x + y = 6$ , $- 3 x - y = 6$ , $(- 1, - 3)$

Step 1

Simplify $3 (- 1) - 3$ .

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Step 1.1

Multiply $3$ by $- 1$ .

$- 3 - 3 = 6$

$- 3 \cdot - 1 - (- 3) = 6$

Step 1.2

Subtract $3$ from $- 3$ .

$- 6 = 6$

$- 3 \cdot - 1 - (- 3) = 6$

$- 6 = 6$

$- 3 \cdot - 1 - (- 3) = 6$

Step 2

Since $- 6 \neq 6$ , there are no solutions.

No solution

Step 3

Simplify $- 3 \cdot - 1 - (- 3)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $- 3$ by $- 1$ .

$3 - (- 3) = 6$

No solution

Step 3.1.2

Multiply $- 1$ by $- 3$ .

$3 + 3 = 6$

No solution

$3 + 3 = 6$

No solution

Step 3.2

Add $3$ and $3$ .

$6 = 6$

No solution

Step 4

Since $6 = 6$ , the equation will always be true.

No solution

Step 5

The ordered pair is not a solution to the system of equations.

$(- 1, - 3)$ is not a solution