Solve by Addition/Elimination 8x+6y=10 , 5x-3y=2.2

$8 x + 6 y = 10$ , $5 x - 3 y = 2.2$

Step 1

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

$8 x + 6 y = 10$

$(2) \cdot (5 x - 3 y) = (2) (2.2)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (5 x - 3 y)$ .

Apply the distributive property.

$8 x + 6 y = 10$

$2 (5 x) + 2 (- 3 y) = (2) (2.2)$

Multiply.

Multiply $5$ by $2$ .

$8 x + 6 y = 10$

$10 x + 2 (- 3 y) = (2) (2.2)$

Multiply $- 3$ by $2$ .

$8 x + 6 y = 10$

$10 x - 6 y = (2) (2.2)$

$8 x + 6 y = 10$

$10 x - 6 y = (2) (2.2)$

$8 x + 6 y = 10$

$10 x - 6 y = (2) (2.2)$

$8 x + 6 y = 10$

$10 x - 6 y = (2) (2.2)$

Simplify the right side.

Multiply $2$ by $2.2$ .

$8 x + 6 y = 10$

$10 x - 6 y = 4.4$

$8 x + 6 y = 10$

$10 x - 6 y = 4.4$

$8 x + 6 y = 10$

$10 x - 6 y = 4.4$

Step 3

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

		$8$	$x$	$+$	$6$	$y$	$=$		$1$	$0$
$+$	$1$	$0$	$x$	$-$	$6$	$y$	$=$	$4$	$.$	$4$
	$1$	$8$	$x$				$=$	$1$	$4$	$.$	$4$

Step 4

Divide each term in $18 x = 14.4$ by $18$ and simplify.

Divide each term in $18 x = 14.4$ by $18$ .

$\frac{18 x}{18} = \frac{14.4}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} = \frac{14.4}{18}$

Divide $x$ by $1$ .

$x = \frac{14.4}{18}$

Simplify the right side.

Divide $14.4$ by $18$ .

$x = 0.8$

Step 5

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 $y$ .

$8 (0.8) + 6 y = 10$

Multiply $8$ by $0.8$ .

$6.4 + 6 y = 10$

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

Subtract $6.4$ from both sides of the equation.

$6 y = 10 - 6.4$

Subtract $6.4$ from $10$ .

$6 y = 3.6$

Divide each term in $6 y = 3.6$ by $6$ and simplify.

Divide each term in $6 y = 3.6$ by $6$ .

$\frac{6 y}{6} = \frac{3.6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{3.6}{6}$

Divide $y$ by $1$ .

$y = \frac{3.6}{6}$

Simplify the right side.

Divide $3.6$ by $6$ .

$y = 0.6$

Step 6

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

$(0.8, 0.6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(0.8, 0.6)$

Equation Form:

$x = 0.8, y = 0.6$

Step 8

Solve by Addition/Elimination 8x+6y=10 , 5x-3y=2.2

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