Solve by Addition/Elimination 3x+2y=4 , 5x-4y=3

$3 x + 2 y = 4$ , $5 x - 4 y = 3$

Step 1

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

$(2) \cdot (3 x + 2 y) = (2) (4)$

$5 x - 4 y = 3$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 (3 x) + 2 (2 y) = (2) (4)$

$5 x - 4 y = 3$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 (2 y) = (2) (4)$

$5 x - 4 y = 3$

Multiply $2$ by $2$ .

$6 x + 4 y = (2) (4)$

$5 x - 4 y = 3$

$6 x + 4 y = (2) (4)$

$5 x - 4 y = 3$

$6 x + 4 y = (2) (4)$

$5 x - 4 y = 3$

$6 x + 4 y = (2) (4)$

$5 x - 4 y = 3$

Simplify the right side.

Multiply $2$ by $4$ .

$6 x + 4 y = 8$

$5 x - 4 y = 3$

$6 x + 4 y = 8$

$5 x - 4 y = 3$

$6 x + 4 y = 8$

$5 x - 4 y = 3$

Step 3

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

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

Step 4

Divide each term in $11 x = 11$ by $11$ and simplify.

Divide each term in $11 x = 11$ by $11$ .

$\frac{11 x}{11} = \frac{11}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{11}{11}$

Divide $x$ by $1$ .

$x = \frac{11}{11}$

Simplify the right side.

Divide $11$ by $11$ .

$x = 1$

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 $y$ .

$6 (1) + 4 y = 8$

Multiply $6$ by $1$ .

$6 + 4 y = 8$

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

Subtract $6$ from both sides of the equation.

$4 y = 8 - 6$

Subtract $6$ from $8$ .

$4 y = 2$

Divide each term in $4 y = 2$ by $4$ and simplify.

Divide each term in $4 y = 2$ by $4$ .

$\frac{4 y}{4} = \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{2}{4}$

Divide $y$ by $1$ .

$y = \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{1}{2}$

Step 6

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

$(1, \frac{1}{2})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, \frac{1}{2})$

Equation Form:

$x = 1, y = \frac{1}{2}$

Step 8

Solve by Addition/Elimination 3x+2y=4 , 5x-4y=3

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