Solve by Addition/Elimination 2x-10y=4 3x-15y=6

$2 x - 10 y = 4$ $3 x - 15 y = 6$

Step 1

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

$(- 3) \cdot (2 x - 10 y) = (- 3) (4)$

$(2) \cdot (3 x - 15 y) = (2) (6)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (2 x - 10 y)$ .

Apply the distributive property.

$- 3 (2 x) - 3 (- 10 y) = (- 3) (4)$

$(2) \cdot (3 x - 15 y) = (2) (6)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (- 10 y) = (- 3) (4)$

$(2) \cdot (3 x - 15 y) = (2) (6)$

Multiply $- 10$ by $- 3$ .

$- 6 x + 30 y = (- 3) (4)$

$(2) \cdot (3 x - 15 y) = (2) (6)$

$- 6 x + 30 y = (- 3) (4)$

$(2) \cdot (3 x - 15 y) = (2) (6)$

$- 6 x + 30 y = (- 3) (4)$

$(2) \cdot (3 x - 15 y) = (2) (6)$

$- 6 x + 30 y = (- 3) (4)$

$(2) \cdot (3 x - 15 y) = (2) (6)$

Simplify the right side.

Multiply $- 3$ by $4$ .

$- 6 x + 30 y = - 12$

$(2) \cdot (3 x - 15 y) = (2) (6)$

$- 6 x + 30 y = - 12$

$(2) \cdot (3 x - 15 y) = (2) (6)$

Simplify the left side.

Simplify $(2) \cdot (3 x - 15 y)$ .

Apply the distributive property.

$- 6 x + 30 y = - 12$

$2 (3 x) + 2 (- 15 y) = (2) (6)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 30 y = - 12$

$6 x + 2 (- 15 y) = (2) (6)$

Multiply $- 15$ by $2$ .

$- 6 x + 30 y = - 12$

$6 x - 30 y = (2) (6)$

$- 6 x + 30 y = - 12$

$6 x - 30 y = (2) (6)$

$- 6 x + 30 y = - 12$

$6 x - 30 y = (2) (6)$

$- 6 x + 30 y = - 12$

$6 x - 30 y = (2) (6)$

Simplify the right side.

Multiply $2$ by $6$ .

$- 6 x + 30 y = - 12$

$6 x - 30 y = 12$

$- 6 x + 30 y = - 12$

$6 x - 30 y = 12$

$- 6 x + 30 y = - 12$

$6 x - 30 y = 12$

Step 3

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

	$-$	$6$	$x$	$+$	$3$	$0$	$y$	$=$	$-$	$1$	$2$
$+$		$6$	$x$	$-$	$3$	$0$	$y$	$=$		$1$	$2$
							$0$	$=$			$0$

Step 4

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Step 5

Solve one of the equations for $y$ .

Add $6 x$ to both sides of the equation.

$30 y = - 12 + 6 x$

Divide each term in $30 y = - 12 + 6 x$ by $30$ and simplify.

Divide each term in $30 y = - 12 + 6 x$ by $30$ .

$\frac{30 y}{30} = \frac{- 12}{30} + \frac{6 x}{30}$

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{30 y}{30} = \frac{- 12}{30} + \frac{6 x}{30}$

Divide $y$ by $1$ .

$y = \frac{- 12}{30} + \frac{6 x}{30}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 12$ and $30$ .

Factor $6$ out of $- 12$ .

$y = \frac{6 (- 2)}{30} + \frac{6 x}{30}$

Cancel the common factors.

Factor $6$ out of $30$ .

$y = \frac{6 \cdot - 2}{6 \cdot 5} + \frac{6 x}{30}$

Cancel the common factor.

$y = \frac{6 \cdot - 2}{6 \cdot 5} + \frac{6 x}{30}$

Rewrite the expression.

$y = \frac{- 2}{5} + \frac{6 x}{30}$

Move the negative in front of the fraction.

$y = - \frac{2}{5} + \frac{6 x}{30}$

Cancel the common factor of $6$ and $30$ .

Factor $6$ out of $6 x$ .

$y = - \frac{2}{5} + \frac{6 (x)}{30}$

Cancel the common factors.

Factor $6$ out of $30$ .

$y = - \frac{2}{5} + \frac{6 x}{6 \cdot 5}$

Cancel the common factor.

$y = - \frac{2}{5} + \frac{6 x}{6 \cdot 5}$

Rewrite the expression.

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

Step 6

The solution is the set of ordered pairs that make $y = - \frac{2}{5} + \frac{x}{5}$ true.

$(x, - \frac{2}{5} + \frac{x}{5})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, - \frac{2}{5} + \frac{x}{5})$

Equation Form:

$x = x, y = - \frac{2}{5} + \frac{x}{5}$

Step 8

Solve by Addition/Elimination 2x-10y=4 3x-15y=6

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