Solve by Addition/Elimination 3y=26-5x 6x+7y=21

$3 y = 26 - 5 x$ $6 x + 7 y = 21$

Simplify the right side.

Reorder $26$ and $- 5 x$ .

$3 y = - 5 x + 26$

$6 x + 7 y = 21$

$3 y = - 5 x + 26$

$6 x + 7 y = 21$

Move all terms containing variables to the left side of the equation.

Add $5 x$ to both sides of the equation.

$3 y + 5 x = 26$

$6 x + 7 y = 21$

Reorder $3 y$ and $5 x$ .

$5 x + 3 y = 26$

$6 x + 7 y = 21$

$5 x + 3 y = 26$

$6 x + 7 y = 21$

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

$(- 7) \cdot (5 x + 3 y) = (- 7) (26)$

$(3) \cdot (6 x + 7 y) = (3) (21)$

Simplify.

Simplify the left side.

Simplify $(- 7) \cdot (5 x + 3 y)$ .

Apply the distributive property.

$- 7 (5 x) - 7 (3 y) = (- 7) (26)$

$(3) \cdot (6 x + 7 y) = (3) (21)$

Multiply.

Multiply $5$ by $- 7$ .

$- 35 x - 7 (3 y) = (- 7) (26)$

$(3) \cdot (6 x + 7 y) = (3) (21)$

Multiply $3$ by $- 7$ .

$- 35 x - 21 y = (- 7) (26)$

$(3) \cdot (6 x + 7 y) = (3) (21)$

$- 35 x - 21 y = (- 7) (26)$

$(3) \cdot (6 x + 7 y) = (3) (21)$

$- 35 x - 21 y = (- 7) (26)$

$(3) \cdot (6 x + 7 y) = (3) (21)$

$- 35 x - 21 y = (- 7) (26)$

$(3) \cdot (6 x + 7 y) = (3) (21)$

Simplify the right side.

Multiply $- 7$ by $26$ .

$- 35 x - 21 y = - 182$

$(3) \cdot (6 x + 7 y) = (3) (21)$

$- 35 x - 21 y = - 182$

$(3) \cdot (6 x + 7 y) = (3) (21)$

Simplify the left side.

Simplify $(3) \cdot (6 x + 7 y)$ .

Apply the distributive property.

$- 35 x - 21 y = - 182$

$3 (6 x) + 3 (7 y) = (3) (21)$

Multiply.

Multiply $6$ by $3$ .

$- 35 x - 21 y = - 182$

$18 x + 3 (7 y) = (3) (21)$

Multiply $7$ by $3$ .

$- 35 x - 21 y = - 182$

$18 x + 21 y = (3) (21)$

$- 35 x - 21 y = - 182$

$18 x + 21 y = (3) (21)$

$- 35 x - 21 y = - 182$

$18 x + 21 y = (3) (21)$

$- 35 x - 21 y = - 182$

$18 x + 21 y = (3) (21)$

Simplify the right side.

Multiply $3$ by $21$ .

$- 35 x - 21 y = - 182$

$18 x + 21 y = 63$

$- 35 x - 21 y = - 182$

$18 x + 21 y = 63$

$- 35 x - 21 y = - 182$

$18 x + 21 y = 63$

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

			$-$	$3$	$5$	$x$	$-$	$2$	$1$	$y$	$=$	$-$	$1$	$8$	$2$
$+$				$1$	$8$	$x$	$+$	$2$	$1$	$y$	$=$			$6$	$3$
			$-$	$1$	$7$	$x$					$=$	$-$	$1$	$1$	$9$

Divide each term in $- 17 x = - 119$ by $- 17$ and simplify.

Divide each term in $- 17 x = - 119$ by $- 17$ .

$\frac{- 17 x}{- 17} = \frac{- 119}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 x}{- 17} = \frac{- 119}{- 17}$

Divide $x$ by $1$ .

$x = \frac{- 119}{- 17}$

$x = \frac{- 119}{- 17}$

$x = \frac{- 119}{- 17}$

Simplify the right side.

Divide $- 119$ by $- 17$ .

$x = 7$

$x = 7$

$x = 7$

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

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

$- 35 \cdot 7 - 21 y = - 182$

Multiply $- 35$ by $7$ .

$- 245 - 21 y = - 182$

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

Add $245$ to both sides of the equation.

$- 21 y = - 182 + 245$

Add $- 182$ and $245$ .

$- 21 y = 63$

$- 21 y = 63$

Divide each term in $- 21 y = 63$ by $- 21$ and simplify.

Divide each term in $- 21 y = 63$ by $- 21$ .

$\frac{- 21 y}{- 21} = \frac{63}{- 21}$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 y}{- 21} = \frac{63}{- 21}$

Divide $y$ by $1$ .

$y = \frac{63}{- 21}$

$y = \frac{63}{- 21}$

$y = \frac{63}{- 21}$

Simplify the right side.

Divide $63$ by $- 21$ .

$y = - 3$

$y = - 3$

$y = - 3$

$y = - 3$

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

$(7, - 3)$

The result can be shown in multiple forms.

Point Form:

$(7, - 3)$

Equation Form:

$x = 7, y = - 3$

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