Solve by Addition/Elimination 8x+7y=15; 6x-5y=1

${\begin{cases} 8 x + 7 y = 15 \\ 6 x - 5 y = 1 \end{cases}$

Step 1

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

$(- 3) \cdot (8 x + 7 y) = (- 3) (15)$

$(4) \cdot (6 x - 5 y) = (4) (1)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (8 x + 7 y)$ .

Apply the distributive property.

$- 3 (8 x) - 3 (7 y) = (- 3) (15)$

$(4) \cdot (6 x - 5 y) = (4) (1)$

Multiply.

Multiply $8$ by $- 3$ .

$- 24 x - 3 (7 y) = (- 3) (15)$

$(4) \cdot (6 x - 5 y) = (4) (1)$

Multiply $7$ by $- 3$ .

$- 24 x - 21 y = (- 3) (15)$

$(4) \cdot (6 x - 5 y) = (4) (1)$

$- 24 x - 21 y = (- 3) (15)$

$(4) \cdot (6 x - 5 y) = (4) (1)$

$- 24 x - 21 y = (- 3) (15)$

$(4) \cdot (6 x - 5 y) = (4) (1)$

$- 24 x - 21 y = (- 3) (15)$

$(4) \cdot (6 x - 5 y) = (4) (1)$

Simplify the right side.

Multiply $- 3$ by $15$ .

$- 24 x - 21 y = - 45$

$(4) \cdot (6 x - 5 y) = (4) (1)$

$- 24 x - 21 y = - 45$

$(4) \cdot (6 x - 5 y) = (4) (1)$

Simplify the left side.

Simplify $(4) \cdot (6 x - 5 y)$ .

Apply the distributive property.

$- 24 x - 21 y = - 45$

$4 (6 x) + 4 (- 5 y) = (4) (1)$

Multiply.

Multiply $6$ by $4$ .

$- 24 x - 21 y = - 45$

$24 x + 4 (- 5 y) = (4) (1)$

Multiply $- 5$ by $4$ .

$- 24 x - 21 y = - 45$

$24 x - 20 y = (4) (1)$

$- 24 x - 21 y = - 45$

$24 x - 20 y = (4) (1)$

$- 24 x - 21 y = - 45$

$24 x - 20 y = (4) (1)$

$- 24 x - 21 y = - 45$

$24 x - 20 y = (4) (1)$

Simplify the right side.

Multiply $4$ by $1$ .

$- 24 x - 21 y = - 45$

$24 x - 20 y = 4$

$- 24 x - 21 y = - 45$

$24 x - 20 y = 4$

$- 24 x - 21 y = - 45$

$24 x - 20 y = 4$

Step 3

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

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

Step 4

Divide each term in $- 41 y = - 41$ by $- 41$ and simplify.

Divide each term in $- 41 y = - 41$ by $- 41$ .

$\frac{- 41 y}{- 41} = \frac{- 41}{- 41}$

Simplify the left side.

Cancel the common factor of $- 41$ .

Cancel the common factor.

$\frac{- 41 y}{- 41} = \frac{- 41}{- 41}$

Divide $y$ by $1$ .

$y = \frac{- 41}{- 41}$

Simplify the right side.

Divide $- 41$ by $- 41$ .

$y = 1$

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 $x$ .

$- 24 x - 21 \cdot 1 = - 45$

Multiply $- 21$ by $1$ .

$- 24 x - 21 = - 45$

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

Add $21$ to both sides of the equation.

$- 24 x = - 45 + 21$

Add $- 45$ and $21$ .

$- 24 x = - 24$

Divide each term in $- 24 x = - 24$ by $- 24$ and simplify.

Divide each term in $- 24 x = - 24$ by $- 24$ .

$\frac{- 24 x}{- 24} = \frac{- 24}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} = \frac{- 24}{- 24}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 24}$

Simplify the right side.

Divide $- 24$ by $- 24$ .

$x = 1$

Step 6

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

$(1, 1)$

Step 7

Solve by Addition/Elimination 8x+7y=15; 6x-5y=1

Related Questions

Support LCMGCF.com by disabling your adblocker.