Finite Math Examples

$21 x - 9 y = 15$ , $7 x = 3 y + 5$

Step 1

Divide each term in $7 x = 3 y + 5$ by $7$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $7 x = 3 y + 5$ by $7$ .

$\frac{7 x}{7} = \frac{3 y}{7} + \frac{5}{7}$

$21 x - 9 y = 15$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{3 y}{7} + \frac{5}{7}$

$21 x - 9 y = 15$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{3 y}{7} + \frac{5}{7}$

$21 x - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$21 x - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$21 x - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$21 x - 9 y = 15$

Step 2

Replace all occurrences of $x$ with $\frac{3 y}{7} + \frac{5}{7}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $21 x - 9 y = 15$ with $\frac{3 y}{7} + \frac{5}{7}$ .

$21 (\frac{3 y}{7} + \frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $21 (\frac{3 y}{7} + \frac{5}{7}) - 9 y$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$21 (\frac{3 y}{7}) + 21 (\frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.2

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.2.1.1.2.1

Factor $7$ out of $21$ .

$7 (3) (\frac{3 y}{7}) + 21 (\frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.2.2

Cancel the common factor.

$7 \cdot (3 (\frac{3 y}{7})) + 21 (\frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.2.3

Rewrite the expression.

$3 (3 y) + 21 (\frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$3 (3 y) + 21 (\frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.3

Multiply $3$ by $3$ .

$9 y + 21 (\frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.4

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.2.1.1.4.1

Factor $7$ out of $21$ .

$9 y + 7 (3) (\frac{5}{7}) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.4.2

Cancel the common factor.

$9 y + 7 \cdot (3 (\frac{5}{7})) - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.4.3

Rewrite the expression.

$9 y + 3 \cdot 5 - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$9 y + 3 \cdot 5 - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.1.5

Multiply $3$ by $5$ .

$9 y + 15 - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$9 y + 15 - 9 y = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.2

Combine the opposite terms in $9 y + 15 - 9 y$ .

Tap for more steps...

Step 2.2.1.2.1

Subtract $9 y$ from $9 y$ .

$0 + 15 = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 2.2.1.2.2

Add $0$ and $15$ .

$15 = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$15 = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$15 = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$15 = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

$15 = 15$

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3 y}{7} + \frac{5}{7}$

Step 4