Solve by Addition/Elimination 8x-5y=11 and 4x-3y=5

$8 x - 5 y = 11$ and $4 x - 3 y = 5$

Step 1

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

$8 x - 5 y = 11$

$(- 2) \cdot (4 x - 3 y) = (- 2) (5)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (4 x - 3 y)$ .

Apply the distributive property.

$8 x - 5 y = 11$

$- 2 (4 x) - 2 (- 3 y) = (- 2) (5)$

Multiply.

Multiply $4$ by $- 2$ .

$8 x - 5 y = 11$

$- 8 x - 2 (- 3 y) = (- 2) (5)$

Multiply $- 3$ by $- 2$ .

$8 x - 5 y = 11$

$- 8 x + 6 y = (- 2) (5)$

$8 x - 5 y = 11$

$- 8 x + 6 y = (- 2) (5)$

$8 x - 5 y = 11$

$- 8 x + 6 y = (- 2) (5)$

$8 x - 5 y = 11$

$- 8 x + 6 y = (- 2) (5)$

Simplify the right side.

Multiply $- 2$ by $5$ .

$8 x - 5 y = 11$

$- 8 x + 6 y = - 10$

$8 x - 5 y = 11$

$- 8 x + 6 y = - 10$

$8 x - 5 y = 11$

$- 8 x + 6 y = - 10$

Step 3

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

		$8$	$x$	$-$	$5$	$y$	$=$		$1$	$1$
$+$	$-$	$8$	$x$	$+$	$6$	$y$	$=$	$-$	$1$	$0$
						$y$	$=$			$1$

Step 4

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 $x$ .

$8 x - 5 \cdot 1 = 11$

Multiply $- 5$ by $1$ .

$8 x - 5 = 11$

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

Add $5$ to both sides of the equation.

$8 x = 11 + 5$

Add $11$ and $5$ .

$8 x = 16$

Divide each term in $8 x = 16$ by $8$ and simplify.

Divide each term in $8 x = 16$ by $8$ .

$\frac{8 x}{8} = \frac{16}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{16}{8}$

Divide $x$ by $1$ .

$x = \frac{16}{8}$

Simplify the right side.

Divide $16$ by $8$ .

$x = 2$

Step 5

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

$(2, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 7

Solve by Addition/Elimination 8x-5y=11 and 4x-3y=5

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