Algebra Examples

$7 x - 5 = 4 y - 6$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$7 x - 5 = 4 (0) - 6$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $4 (0) - 6$ .

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Step 1.2.1.1

Multiply $4$ by $0$ .

$7 x - 5 = 0 - 6$

Step 1.2.1.2

Subtract $6$ from $0$ .

$7 x - 5 = - 6$

Step 1.2.2

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

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Step 1.2.2.1

Add $5$ to both sides of the equation.

$7 x = - 6 + 5$

Step 1.2.2.2

Add $- 6$ and $5$ .

$7 x = - 1$

Step 1.2.3

Divide each term in $7 x = - 1$ by $7$ and simplify.

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Step 1.2.3.1

Divide each term in $7 x = - 1$ by $7$ .

$\frac{7 x}{7} = \frac{- 1}{7}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $7$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 1}{7}$

Step 1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{7}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{7}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{7}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$7 (0) - 5 = 4 y - 6$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $4 y - 6 = 7 (0) - 5$ .

$4 y - 6 = 7 (0) - 5$

Step 2.2.2

Simplify $7 (0) - 5$ .

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Step 2.2.2.1

Multiply $7$ by $0$ .

$4 y - 6 = 0 - 5$

Step 2.2.2.2

Subtract $5$ from $0$ .

$4 y - 6 = - 5$

Step 2.2.3

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

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Step 2.2.3.1

Add $6$ to both sides of the equation.

$4 y = - 5 + 6$

Step 2.2.3.2

Add $- 5$ and $6$ .

$4 y = 1$

Step 2.2.4

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

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Step 2.2.4.1

Divide each term in $4 y = 1$ by $4$ .

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

Step 2.2.4.2

Simplify the left side.

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Step 2.2.4.2.1

Cancel the common factor of $4$ .

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Step 2.2.4.2.1.1

Cancel the common factor.

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

Step 2.2.4.2.1.2

Divide $y$ by $1$ .

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

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{4})$

Step 3

List the intersections.

x-intercept(s): $(- \frac{1}{7}, 0)$

y-intercept(s): $(0, \frac{1}{4})$

Step 4