Algebra Examples

$3 y = 9 x - 6$ $2 y + 6 x = 4$

Step 1

Solve the system of equations.

Tap for more steps...

Step 1.1

Simplify the left side.

Tap for more steps...

Step 1.1.1

Reorder $2 y$ and $6 x$ .

$6 x + 2 y = 4$

$3 y = 9 x - 6$

$6 x + 2 y = 4$

$3 y = 9 x - 6$

Step 1.2

Subtract $9 x$ from both sides of the equation.

$3 y - 9 x = - 6, 6 x + 2 y = 4$

Step 1.3

Reorder the polynomial.

$- 9 x + 3 y = - 6$

$6 x + 2 y = 4$

Step 1.4

Multiply each equation by the value that makes the coefficients of $y$ opposite.

$(- 2) \cdot (- 9 x + 3 y) = (- 2) (- 6)$

$(3) \cdot (6 x + 2 y) = (3) (4)$

Step 1.5

Simplify.

Tap for more steps...

Step 1.5.1

Simplify the left side.

Tap for more steps...

Step 1.5.1.1

Simplify $(- 2) \cdot (- 9 x + 3 y)$ .

Tap for more steps...

Step 1.5.1.1.1

Apply the distributive property.

$- 2 (- 9 x) - 2 (3 y) = (- 2) (- 6)$

$(3) \cdot (6 x + 2 y) = (3) (4)$

Step 1.5.1.1.2

Multiply.

Tap for more steps...

Step 1.5.1.1.2.1

Multiply $- 9$ by $- 2$ .

$18 x - 2 (3 y) = (- 2) (- 6)$

$(3) \cdot (6 x + 2 y) = (3) (4)$

Step 1.5.1.1.2.2

Multiply $3$ by $- 2$ .

$18 x - 6 y = (- 2) (- 6)$

$(3) \cdot (6 x + 2 y) = (3) (4)$

$18 x - 6 y = (- 2) (- 6)$

$(3) \cdot (6 x + 2 y) = (3) (4)$

$18 x - 6 y = (- 2) (- 6)$

$(3) \cdot (6 x + 2 y) = (3) (4)$

$18 x - 6 y = (- 2) (- 6)$

$(3) \cdot (6 x + 2 y) = (3) (4)$

Step 1.5.2

Simplify the right side.

Tap for more steps...

Step 1.5.2.1

Multiply $- 2$ by $- 6$ .

$18 x - 6 y = 12$

$(3) \cdot (6 x + 2 y) = (3) (4)$

$18 x - 6 y = 12$

$(3) \cdot (6 x + 2 y) = (3) (4)$

Step 1.5.3

Simplify the left side.

Tap for more steps...

Step 1.5.3.1

Simplify $(3) \cdot (6 x + 2 y)$ .

Tap for more steps...

Step 1.5.3.1.1

Apply the distributive property.

$18 x - 6 y = 12$

$3 (6 x) + 3 (2 y) = (3) (4)$

Step 1.5.3.1.2

Multiply.

Tap for more steps...

Step 1.5.3.1.2.1

Multiply $6$ by $3$ .

$18 x - 6 y = 12$

$18 x + 3 (2 y) = (3) (4)$

Step 1.5.3.1.2.2

Multiply $2$ by $3$ .

$18 x - 6 y = 12$

$18 x + 6 y = (3) (4)$

$18 x - 6 y = 12$

$18 x + 6 y = (3) (4)$

$18 x - 6 y = 12$

$18 x + 6 y = (3) (4)$

$18 x - 6 y = 12$

$18 x + 6 y = (3) (4)$

Step 1.5.4

Simplify the right side.

Tap for more steps...

Step 1.5.4.1

Multiply $3$ by $4$ .

$18 x - 6 y = 12$

$18 x + 6 y = 12$

$18 x - 6 y = 12$

$18 x + 6 y = 12$

$18 x - 6 y = 12$

$18 x + 6 y = 12$

Step 1.6

Add the two equations together to eliminate $y$ from the system.

	$1$	$8$	$x$	$-$	$6$	$y$	$=$	$1$	$2$
$+$	$1$	$8$	$x$	$+$	$6$	$y$	$=$	$1$	$2$
	$3$	$6$	$x$				$=$	$2$	$4$

Step 1.7

Divide each term in $36 x = 24$ by $36$ and simplify.

Tap for more steps...

Step 1.7.1

Divide each term in $36 x = 24$ by $36$ .

$\frac{36 x}{36} = \frac{24}{36}$

Step 1.7.2

Simplify the left side.

Tap for more steps...

Step 1.7.2.1

Cancel the common factor of $36$ .

Tap for more steps...

Step 1.7.2.1.1

Cancel the common factor.

$\frac{36 x}{36} = \frac{24}{36}$

Step 1.7.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{36}$

Step 1.7.3

Simplify the right side.

Tap for more steps...

Step 1.7.3.1

Cancel the common factor of $24$ and $36$ .

Tap for more steps...

Step 1.7.3.1.1

Factor $12$ out of $24$ .

$x = \frac{12 (2)}{36}$

Step 1.7.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.7.3.1.2.1

Factor $12$ out of $36$ .

$x = \frac{12 \cdot 2}{12 \cdot 3}$

Step 1.7.3.1.2.2

Cancel the common factor.

$x = \frac{12 \cdot 2}{12 \cdot 3}$

Step 1.7.3.1.2.3

Rewrite the expression.

$x = \frac{2}{3}$

Step 1.8

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

Tap for more steps...

Step 1.8.1

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$18 (\frac{2}{3}) - 6 y = 12$

Step 1.8.2

Simplify each term.

Tap for more steps...

Step 1.8.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.8.2.1.1

Factor $3$ out of $18$ .

$3 (6) \frac{2}{3} - 6 y = 12$

Step 1.8.2.1.2

Cancel the common factor.

$3 \cdot 6 \frac{2}{3} - 6 y = 12$

Step 1.8.2.1.3

Rewrite the expression.

$6 \cdot 2 - 6 y = 12$

Step 1.8.2.2

Multiply $6$ by $2$ .

$12 - 6 y = 12$

Step 1.8.3

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

Tap for more steps...

Step 1.8.3.1

Subtract $12$ from both sides of the equation.

$- 6 y = 12 - 12$

Step 1.8.3.2

Subtract $12$ from $12$ .

$- 6 y = 0$

Step 1.8.4

Divide each term in $- 6 y = 0$ by $- 6$ and simplify.

Tap for more steps...

Step 1.8.4.1

Divide each term in $- 6 y = 0$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Step 1.8.4.2

Simplify the left side.

Tap for more steps...

Step 1.8.4.2.1

Cancel the common factor of $- 6$ .

Tap for more steps...

Step 1.8.4.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Step 1.8.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{- 6}$

Step 1.8.4.3

Simplify the right side.

Tap for more steps...

Step 1.8.4.3.1

Divide $0$ by $- 6$ .

$y = 0$

Step 1.9

The solution to the independent system of equations can be represented as a point.

$(\frac{2}{3}, 0)$

Step 2

Since the system has a point of intersection, the system is independent.

Independent

Step 3

	$1$	$8$	$x$	$-$	$6$	$y$	$=$	$1$	$2$
$+$	$1$	$8$	$x$	$+$	$6$	$y$	$=$	$1$	$2$
	$3$	$6$	$x$				$=$	$2$	$4$

	$1$	$8$	$x$	$-$	$6$	$y$	$=$	$1$	$2$
$+$	$1$	$8$	$x$	$+$	$6$	$y$	$=$	$1$	$2$
	$3$	$6$	$x$				$=$	$2$	$4$

	$1$	$8$	$x$	$-$	$6$	$y$	$=$	$1$	$2$
$+$	$1$	$8$	$x$	$+$	$6$	$y$	$=$	$1$	$2$
	$3$	$6$	$x$				$=$	$2$	$4$