Solve by Addition/Elimination 5x-2y=4 , -35x+14y=-28

$5 x - 2 y = 4$ , $- 35 x + 14 y = - 28$

Step 1

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

$(7) \cdot (5 x - 2 y) = (7) (4)$

$- 35 x + 14 y = - 28$

Step 2

Simplify.

Simplify the left side.

Simplify $(7) \cdot (5 x - 2 y)$ .

Apply the distributive property.

$7 (5 x) + 7 (- 2 y) = (7) (4)$

$- 35 x + 14 y = - 28$

Multiply.

Multiply $5$ by $7$ .

$35 x + 7 (- 2 y) = (7) (4)$

$- 35 x + 14 y = - 28$

Multiply $- 2$ by $7$ .

$35 x - 14 y = (7) (4)$

$- 35 x + 14 y = - 28$

$35 x - 14 y = (7) (4)$

$- 35 x + 14 y = - 28$

$35 x - 14 y = (7) (4)$

$- 35 x + 14 y = - 28$

$35 x - 14 y = (7) (4)$

$- 35 x + 14 y = - 28$

Simplify the right side.

Multiply $7$ by $4$ .

$35 x - 14 y = 28$

$- 35 x + 14 y = - 28$

$35 x - 14 y = 28$

$- 35 x + 14 y = - 28$

$35 x - 14 y = 28$

$- 35 x + 14 y = - 28$

Step 3

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

		$3$	$5$	$x$	$-$	$1$	$4$	$y$	$=$		$2$	$8$
$+$	$-$	$3$	$5$	$x$	$+$	$1$	$4$	$y$	$=$	$-$	$2$	$8$
								$0$	$=$			$0$

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 $35 x$ from both sides of the equation.

$- 14 y = 28 - 35 x$

Divide each term in $- 14 y = 28 - 35 x$ by $- 14$ and simplify.

Divide each term in $- 14 y = 28 - 35 x$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{28}{- 14} + \frac{- 35 x}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{28}{- 14} + \frac{- 35 x}{- 14}$

Divide $y$ by $1$ .

$y = \frac{28}{- 14} + \frac{- 35 x}{- 14}$

Simplify the right side.

Simplify each term.

Divide $28$ by $- 14$ .

$y = - 2 + \frac{- 35 x}{- 14}$

Cancel the common factor of $- 35$ and $- 14$ .

Factor $- 7$ out of $- 35 x$ .

$y = - 2 + \frac{- 7 (5 x)}{- 14}$

Cancel the common factors.

Factor $- 7$ out of $- 14$ .

$y = - 2 + \frac{- 7 (5 x)}{- 7 (2)}$

Cancel the common factor.

$y = - 2 + \frac{- 7 (5 x)}{- 7 \cdot 2}$

Rewrite the expression.

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

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Point Form:

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

Equation Form:

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

Step 8

Solve by Addition/Elimination 5x-2y=4 , -35x+14y=-28

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