Algebra Examples

$7 x - 5 = 4 y - 6$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $4 y - 6 = 7 x - 5$ .

$4 y - 6 = 7 x - 5$

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 $6$ to both sides of the equation.

$4 y = 7 x - 5 + 6$

Step 1.2.2

Add $- 5$ and $6$ .

$4 y = 7 x + 1$

Step 1.3

Divide each term in $4 y = 7 x + 1$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 y = 7 x + 1$ by $4$ .

$\frac{4 y}{4} = \frac{7 x}{4} + \frac{1}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{7 x}{4} + \frac{1}{4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{7 x}{4} + \frac{1}{4}$

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

Remove parentheses.

$y = \frac{7 (0)}{4} + \frac{1}{4}$

Step 3.2

Simplify $\frac{7 (0)}{4} + \frac{1}{4}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{7 (0) + 1}{4}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $7$ by $0$ .

$y = \frac{0 + 1}{4}$

Step 3.2.2.2

Add $0$ and $1$ .

$y = \frac{1}{4}$

Step 3.3

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

$(0, \frac{1}{4})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{7 (1)}{4} + \frac{1}{4}$

Step 4.2

Simplify $\frac{7 (1)}{4} + \frac{1}{4}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{7 (1) + 1}{4}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $7$ by $1$ .

$y = \frac{7 + 1}{4}$

Step 4.2.2.2

Add $7$ and $1$ .

$y = \frac{8}{4}$

Step 4.2.2.3

Divide $8$ by $4$ .

$y = 2$

Step 4.3

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

Remove parentheses.

$y = \frac{7 (2)}{4} + \frac{1}{4}$

Step 5.2

Simplify $\frac{7 (2)}{4} + \frac{1}{4}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{7 (2) + 1}{4}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $7$ by $2$ .

$y = \frac{14 + 1}{4}$

Step 5.2.2.2

Add $14$ and $1$ .

$y = \frac{15}{4}$

Step 5.3

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

$(2, \frac{15}{4})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{1}{4}), (1, 2), (2, \frac{15}{4})$

Step 7