Algebra Examples

$y = 2 x - 11$ $- 3 y = - 6 x - 15$

Step 1

Replace all occurrences of $y$ with $2 x - 11$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $- 3 y = - 6 x - 15$ with $2 x - 11$ .

$- 3 (2 x - 11) = - 6 x - 15$

$y = 2 x - 11$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $- 3 (2 x - 11)$ .

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Step 1.2.1.1

Apply the distributive property.

$- 3 (2 x) - 3 \cdot - 11 = - 6 x - 15$

$y = 2 x - 11$

Step 1.2.1.2

Multiply.

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Step 1.2.1.2.1

Multiply $2$ by $- 3$ .

$- 6 x - 3 \cdot - 11 = - 6 x - 15$

$y = 2 x - 11$

Step 1.2.1.2.2

Multiply $- 3$ by $- 11$ .

$- 6 x + 33 = - 6 x - 15$

$y = 2 x - 11$

$- 6 x + 33 = - 6 x - 15$

$y = 2 x - 11$

$- 6 x + 33 = - 6 x - 15$

$y = 2 x - 11$

$- 6 x + 33 = - 6 x - 15$

$y = 2 x - 11$

$- 6 x + 33 = - 6 x - 15$

$y = 2 x - 11$

Step 2

Solve for $x$ in $- 6 x + 33 = - 6 x - 15$ .

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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

Add $6 x$ to both sides of the equation.

$- 6 x + 33 + 6 x = - 15$

$y = 2 x - 11$

Step 2.1.2

Combine the opposite terms in $- 6 x + 33 + 6 x$ .

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Step 2.1.2.1

Add $- 6 x$ and $6 x$ .

$0 + 33 = - 15$

$y = 2 x - 11$

Step 2.1.2.2

Add $0$ and $33$ .

$33 = - 15$

$y = 2 x - 11$

$33 = - 15$

$y = 2 x - 11$

$33 = - 15$

$y = 2 x - 11$

Step 2.2

Since $33 \neq - 15$ , there are no solutions.

No solution

$y = 2 x - 11$

No solution

Step 3