Algebra Examples

$Y - 6 X = 2 (X - 3)$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $2 (X - 3)$ .

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Step 1.1.1

Rewrite.

$Y - 6 X = 0 + 0 + 2 (X - 3)$

Step 1.1.2

Simplify by adding zeros.

$Y - 6 X = 2 (X - 3)$

Step 1.1.3

Apply the distributive property.

$Y - 6 X = 2 X + 2 \cdot - 3$

Step 1.1.4

Multiply $2$ by $- 3$ .

$Y - 6 X = 2 X - 6$

Step 1.2

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

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Step 1.2.1

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

$Y = 2 X - 6 + 6 X$

Step 1.2.2

Add $2 X$ and $6 X$ .

$Y = 8 X - 6$

Step 2

Choose any value for $X$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $X$ to find the ordered pair.

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Step 3.1

Simplify $8 (0) - 6$ .

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Step 3.1.1

Multiply $8$ by $0$ .

$Y = 0 - 6$

Step 3.1.2

Subtract $6$ from $0$ .

$Y = - 6$

Step 3.2

Use the $X$ and $y$ values to form the ordered pair.

$(0, - 6)$

Step 4

Choose $1$ to substitute in for $X$ to find the ordered pair.

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Step 4.1

Simplify $8 (1) - 6$ .

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Step 4.1.1

Multiply $8$ by $1$ .

$Y = 8 - 6$

Step 4.1.2

Subtract $6$ from $8$ .

$Y = 2$

Step 4.2

Use the $X$ and $y$ values to form the ordered pair.

$(1, 2)$

Step 5

Choose $2$ to substitute in for $X$ to find the ordered pair.

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Step 5.1

Simplify $8 (2) - 6$ .

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Step 5.1.1

Multiply $8$ by $2$ .

$Y = 16 - 6$

Step 5.1.2

Subtract $6$ from $16$ .

$Y = 10$

Step 5.2

Use the $X$ and $y$ values to form the ordered pair.

$(2, 10)$

Step 6

These are three possible solutions to the equation.

$(0, - 6), (1, 2), (2, 10)$

Step 7