Solve by Addition/Elimination 4x-5y=1 , -8x+10y=-2

$4 x - 5 y = 1$ , $- 8 x + 10 y = - 2$

Step 1

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

$(2) \cdot (4 x - 5 y) = (2) (1)$

$- 8 x + 10 y = - 2$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (4 x - 5 y)$ .

Apply the distributive property.

$2 (4 x) + 2 (- 5 y) = (2) (1)$

$- 8 x + 10 y = - 2$

Multiply.

Multiply $4$ by $2$ .

$8 x + 2 (- 5 y) = (2) (1)$

$- 8 x + 10 y = - 2$

Multiply $- 5$ by $2$ .

$8 x - 10 y = (2) (1)$

$- 8 x + 10 y = - 2$

$8 x - 10 y = (2) (1)$

$- 8 x + 10 y = - 2$

$8 x - 10 y = (2) (1)$

$- 8 x + 10 y = - 2$

$8 x - 10 y = (2) (1)$

$- 8 x + 10 y = - 2$

Simplify the right side.

Multiply $2$ by $1$ .

$8 x - 10 y = 2$

$- 8 x + 10 y = - 2$

$8 x - 10 y = 2$

$- 8 x + 10 y = - 2$

$8 x - 10 y = 2$

$- 8 x + 10 y = - 2$

Step 3

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

		$8$	$x$	$-$	$1$	$0$	$y$	$=$		$2$
$+$	$-$	$8$	$x$	$+$	$1$	$0$	$y$	$=$	$-$	$2$
							$0$	$=$		$0$

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 $y$ .

Subtract $8 x$ from both sides of the equation.

$- 10 y = 2 - 8 x$

Divide each term in $- 10 y = 2 - 8 x$ by $- 10$ and simplify.

Divide each term in $- 10 y = 2 - 8 x$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{2}{- 10} + \frac{- 8 x}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{2}{- 10} + \frac{- 8 x}{- 10}$

Divide $y$ by $1$ .

$y = \frac{2}{- 10} + \frac{- 8 x}{- 10}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $- 10$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 10} + \frac{- 8 x}{- 10}$

Cancel the common factors.

Factor $2$ out of $- 10$ .

$y = \frac{2 \cdot 1}{2 \cdot - 5} + \frac{- 8 x}{- 10}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 5} + \frac{- 8 x}{- 10}$

Rewrite the expression.

$y = \frac{1}{- 5} + \frac{- 8 x}{- 10}$

Move the negative in front of the fraction.

$y = - \frac{1}{5} + \frac{- 8 x}{- 10}$

Cancel the common factor of $- 8$ and $- 10$ .

Factor $- 2$ out of $- 8 x$ .

$y = - \frac{1}{5} + \frac{- 2 (4 x)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$y = - \frac{1}{5} + \frac{- 2 (4 x)}{- 2 (5)}$

Cancel the common factor.

$y = - \frac{1}{5} + \frac{- 2 (4 x)}{- 2 \cdot 5}$

Rewrite the expression.

$y = - \frac{1}{5} + \frac{4 x}{5}$

Step 6

The solution is the set of ordered pairs that make $y = - \frac{1}{5} + \frac{4 x}{5}$ true.

$(x, - \frac{1}{5} + \frac{4 x}{5})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, - \frac{1}{5} + \frac{4 x}{5})$

Equation Form:

$x = x, y = - \frac{1}{5} + \frac{4 x}{5}$

Step 8

Solve by Addition/Elimination 4x-5y=1 , -8x+10y=-2

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