Solve by Addition/Elimination 3x+7y=19 -2x+7y=34

$3 x + 7 y = 19$ $- 2 x + 7 y = 34$

Step 1

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

$(2) \cdot (3 x + 7 y) = (2) (19)$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (3 x + 7 y)$ .

Apply the distributive property.

$2 (3 x) + 2 (7 y) = (2) (19)$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 (7 y) = (2) (19)$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

Multiply $7$ by $2$ .

$6 x + 14 y = (2) (19)$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

$6 x + 14 y = (2) (19)$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

$6 x + 14 y = (2) (19)$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

$6 x + 14 y = (2) (19)$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

Simplify the right side.

Multiply $2$ by $19$ .

$6 x + 14 y = 38$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

$6 x + 14 y = 38$

$(3) \cdot (- 2 x + 7 y) = (3) (34)$

Simplify the left side.

Simplify $(3) \cdot (- 2 x + 7 y)$ .

Apply the distributive property.

$6 x + 14 y = 38$

$3 (- 2 x) + 3 (7 y) = (3) (34)$

Multiply.

Multiply $- 2$ by $3$ .

$6 x + 14 y = 38$

$- 6 x + 3 (7 y) = (3) (34)$

Multiply $7$ by $3$ .

$6 x + 14 y = 38$

$- 6 x + 21 y = (3) (34)$

$6 x + 14 y = 38$

$- 6 x + 21 y = (3) (34)$

$6 x + 14 y = 38$

$- 6 x + 21 y = (3) (34)$

$6 x + 14 y = 38$

$- 6 x + 21 y = (3) (34)$

Simplify the right side.

Multiply $3$ by $34$ .

$6 x + 14 y = 38$

$- 6 x + 21 y = 102$

$6 x + 14 y = 38$

$- 6 x + 21 y = 102$

$6 x + 14 y = 38$

$- 6 x + 21 y = 102$

Step 3

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

		$6$	$x$	$+$	$1$	$4$	$y$	$=$		$3$	$8$
$+$	$-$	$6$	$x$	$+$	$2$	$1$	$y$	$=$	$1$	$0$	$2$
					$3$	$5$	$y$	$=$	$1$	$4$	$0$

Step 4

Divide each term in $35 y = 140$ by $35$ and simplify.

Divide each term in $35 y = 140$ by $35$ .

$\frac{35 y}{35} = \frac{140}{35}$

Simplify the left side.

Cancel the common factor of $35$ .

Cancel the common factor.

$\frac{35 y}{35} = \frac{140}{35}$

Divide $y$ by $1$ .

$y = \frac{140}{35}$

Simplify the right side.

Divide $140$ by $35$ .

$y = 4$

Step 5

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

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

$6 x + 14 (4) = 38$

Multiply $14$ by $4$ .

$6 x + 56 = 38$

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

Subtract $56$ from both sides of the equation.

$6 x = 38 - 56$

Subtract $56$ from $38$ .

$6 x = - 18$

Divide each term in $6 x = - 18$ by $6$ and simplify.

Divide each term in $6 x = - 18$ by $6$ .

$\frac{6 x}{6} = \frac{- 18}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 18}{6}$

Divide $x$ by $1$ .

$x = \frac{- 18}{6}$

Simplify the right side.

Divide $- 18$ by $6$ .

$x = - 3$

Step 6

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

$(- 3, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 3, 4)$

Equation Form:

$x = - 3, y = 4$

Step 8

Solve by Addition/Elimination 3x+7y=19 -2x+7y=34

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