Pre-Algebra Examples

$x - 3 y = 3$ , $x + 3 y = 9$ , $y = 6$

Step 1

Replace all occurrences of $y$ with $6$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $x - 3 y = 3$ with $6$ .

$x - 3 \cdot 6 = 3$

$y = 6$

$x + 3 y = 9$

Step 1.2

Simplify the left side.

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Step 1.2.1

Multiply $- 3$ by $6$ .

$x - 18 = 3$

$y = 6$

$x + 3 y = 9$

$x - 18 = 3$

$y = 6$

$x + 3 y = 9$

Step 1.3

Replace all occurrences of $y$ in $x + 3 y = 9$ with $6$ .

$x + 3 (6) = 9$

$x - 18 = 3$

$y = 6$

Step 1.4

Simplify the left side.

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Step 1.4.1

Multiply $3$ by $6$ .

$x + 18 = 9$

$x - 18 = 3$

$y = 6$

$x + 18 = 9$

$x - 18 = 3$

$y = 6$

$x + 18 = 9$

$x - 18 = 3$

$y = 6$

Step 2

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

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Step 2.1

Subtract $18$ from both sides of the equation.

$x = 9 - 18$

$x - 18 = 3$

$y = 6$

Step 2.2

Subtract $18$ from $9$ .

$x = - 9$

$x - 18 = 3$

$y = 6$

$x = - 9$

$x - 18 = 3$

$y = 6$

Step 3

Replace all occurrences of $x$ with $- 9$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $x - 18 = 3$ with $- 9$ .

$(- 9) - 18 = 3$

$x = - 9$

$y = 6$

Step 3.2

Simplify the left side.

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Step 3.2.1

Subtract $18$ from $- 9$ .

$- 27 = 3$

$x = - 9$

$y = 6$

$- 27 = 3$

$x = - 9$

$y = 6$

$- 27 = 3$

$x = - 9$

$y = 6$

Step 4

Since $- 27 = 3$ is not true, there is no solution.

No solution

Step 5