Algebra Examples

$7 x + 3 = 5$ and $y - 1 = 6$

Step 1

Solve for $x$ in $7 x + 3 = 5$ .

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Step 1.1

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

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Step 1.1.1

Subtract $3$ from both sides of the equation.

$7 x = 5 - 3$

$y - 1 = 6$

Step 1.1.2

Subtract $3$ from $5$ .

$7 x = 2$

$y - 1 = 6$

$7 x = 2$

$y - 1 = 6$

Step 1.2

Divide each term in $7 x = 2$ by $7$ and simplify.

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Step 1.2.1

Divide each term in $7 x = 2$ by $7$ .

$\frac{7 x}{7} = \frac{2}{7}$

$y - 1 = 6$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $7$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{2}{7}$

$y - 1 = 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{7}$

$y - 1 = 6$

$x = \frac{2}{7}$

$y - 1 = 6$

$x = \frac{2}{7}$

$y - 1 = 6$

$x = \frac{2}{7}$

$y - 1 = 6$

$x = \frac{2}{7}$

$y - 1 = 6$

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$y = 6 + 1$

$x = \frac{2}{7}$

Step 2.2

Add $6$ and $1$ .

$y = 7$

$x = \frac{2}{7}$

$y = 7$

$x = \frac{2}{7}$

Step 3

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{2}{7}, 7)$

Step 4

The result can be shown in multiple forms.

Point Form:

$(\frac{2}{7}, 7)$

Equation Form:

$x = \frac{2}{7}, y = 7$

Step 5