Finite Math Examples

$3 x - 2 y = 5$ , $6 x - 4 y = - 6$

Step 1

Solve for $x$ in $3 x - 2 y = 5$ .

Tap for more steps...

Step 1.1

Add $2 y$ to both sides of the equation.

$3 x = 5 + 2 y$

$6 x - 4 y = - 6$

Step 1.2

Divide each term in $3 x = 5 + 2 y$ by $3$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $3 x = 5 + 2 y$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3} + \frac{2 y}{3}$

$6 x - 4 y = - 6$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3} + \frac{2 y}{3}$

$6 x - 4 y = - 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{3} + \frac{2 y}{3}$

$6 x - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$6 x - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$6 x - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$6 x - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$6 x - 4 y = - 6$

Step 2

Replace all occurrences of $x$ with $\frac{5}{3} + \frac{2 y}{3}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $6 x - 4 y = - 6$ with $\frac{5}{3} + \frac{2 y}{3}$ .

$6 (\frac{5}{3} + \frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $6 (\frac{5}{3} + \frac{2 y}{3}) - 4 y$ .

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.

$6 (\frac{5}{3}) + 6 (\frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1.2.1

Factor $3$ out of $6$ .

$3 (2) (\frac{5}{3}) + 6 (\frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.2.2

Cancel the common factor.

$3 \cdot (2 (\frac{5}{3})) + 6 (\frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.2.3

Rewrite the expression.

$2 \cdot 5 + 6 (\frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$2 \cdot 5 + 6 (\frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.3

Multiply $2$ by $5$ .

$10 + 6 (\frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1.4.1

Factor $3$ out of $6$ .

$10 + 3 (2) (\frac{2 y}{3}) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.4.2

Cancel the common factor.

$10 + 3 \cdot (2 (\frac{2 y}{3})) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.4.3

Rewrite the expression.

$10 + 2 (2 y) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$10 + 2 (2 y) - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.1.5

Multiply $2$ by $2$ .

$10 + 4 y - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$10 + 4 y - 4 y = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.2

Combine the opposite terms in $10 + 4 y - 4 y$ .

Tap for more steps...

Step 2.2.1.2.1

Subtract $4 y$ from $4 y$ .

$10 + 0 = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 2.2.1.2.2

Add $10$ and $0$ .

$10 = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$10 = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$10 = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$10 = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

$10 = - 6$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 3

Since $10 = - 6$ is not true, there is no solution.

No solution

Step 4