Solve by Addition/Elimination 3x+4y=0 , 2x+3y=1

$3 x + 4 y = 0$ , $2 x + 3 y = 1$

Step 1

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

$(- 2) \cdot (3 x + 4 y) = (- 2) (0)$

$(3) \cdot (2 x + 3 y) = (3) (1)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 (3 x) - 2 (4 y) = (- 2) (0)$

$(3) \cdot (2 x + 3 y) = (3) (1)$

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 (4 y) = (- 2) (0)$

$(3) \cdot (2 x + 3 y) = (3) (1)$

Multiply $4$ by $- 2$ .

$- 6 x - 8 y = (- 2) (0)$

$(3) \cdot (2 x + 3 y) = (3) (1)$

$- 6 x - 8 y = (- 2) (0)$

$(3) \cdot (2 x + 3 y) = (3) (1)$

$- 6 x - 8 y = (- 2) (0)$

$(3) \cdot (2 x + 3 y) = (3) (1)$

$- 6 x - 8 y = (- 2) (0)$

$(3) \cdot (2 x + 3 y) = (3) (1)$

Simplify the right side.

Multiply $- 2$ by $0$ .

$- 6 x - 8 y = 0$

$(3) \cdot (2 x + 3 y) = (3) (1)$

$- 6 x - 8 y = 0$

$(3) \cdot (2 x + 3 y) = (3) (1)$

Simplify the left side.

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

Apply the distributive property.

$- 6 x - 8 y = 0$

$3 (2 x) + 3 (3 y) = (3) (1)$

Multiply.

Multiply $2$ by $3$ .

$- 6 x - 8 y = 0$

$6 x + 3 (3 y) = (3) (1)$

Multiply $3$ by $3$ .

$- 6 x - 8 y = 0$

$6 x + 9 y = (3) (1)$

$- 6 x - 8 y = 0$

$6 x + 9 y = (3) (1)$

$- 6 x - 8 y = 0$

$6 x + 9 y = (3) (1)$

$- 6 x - 8 y = 0$

$6 x + 9 y = (3) (1)$

Simplify the right side.

Multiply $3$ by $1$ .

$- 6 x - 8 y = 0$

$6 x + 9 y = 3$

$- 6 x - 8 y = 0$

$6 x + 9 y = 3$

$- 6 x - 8 y = 0$

$6 x + 9 y = 3$

Step 3

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

	$-$	$6$	$x$	$-$	$8$	$y$	$=$	$0$
$+$		$6$	$x$	$+$	$9$	$y$	$=$	$3$
						$y$	$=$	$3$

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 $x$ .

$- 6 x - 8 \cdot 3 = 0$

Multiply $- 8$ by $3$ .

$- 6 x - 24 = 0$

Add $24$ to both sides of the equation.

$- 6 x = 24$

Divide each term in $- 6 x = 24$ by $- 6$ and simplify.

Divide each term in $- 6 x = 24$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{24}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{24}{- 6}$

Divide $x$ by $1$ .

$x = \frac{24}{- 6}$

Simplify the right side.

Divide $24$ by $- 6$ .

$x = - 4$

Step 5

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

$(- 4, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, 3)$

Equation Form:

$x = - 4, y = 3$

Step 7

Solve by Addition/Elimination 3x+4y=0 , 2x+3y=1

Related Questions

Support LCMGCF.com by disabling your adblocker.