Solve by Addition/Elimination -3x-4y=7 -2x+4y=3

$- 3 x - 4 y = 7$ $- 2 x + 4 y = 3$

Step 1

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

	$-$	$3$	$x$	$-$	$4$	$y$	$=$	$7$
$+$	$-$	$2$	$x$	$+$	$4$	$y$	$=$	$3$
	$-$	$5$	$x$				$=$	$1$	$0$

Step 2

Divide each term in $- 5 x = 10$ by $- 5$ and simplify.

Divide each term in $- 5 x = 10$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{10}{- 5}$

Divide $x$ by $1$ .

$x = \frac{10}{- 5}$

Simplify the right side.

Divide $10$ by $- 5$ .

$x = - 2$

Step 3

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 $y$ .

$- 3 \cdot - 2 - 4 y = 7$

Multiply $- 3$ by $- 2$ .

$6 - 4 y = 7$

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

Subtract $6$ from both sides of the equation.

$- 4 y = 7 - 6$

Subtract $6$ from $7$ .

$- 4 y = 1$

Divide each term in $- 4 y = 1$ by $- 4$ and simplify.

Divide each term in $- 4 y = 1$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{1}{- 4}$

Divide $y$ by $1$ .

$y = \frac{1}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{1}{4}$

Step 4

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

$(- 2, - \frac{1}{4})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, - \frac{1}{4})$

Equation Form:

$x = - 2, y = - \frac{1}{4}$

Step 6

Solve by Addition/Elimination -3x-4y=7 -2x+4y=3

Related Questions

Support LCMGCF.com by disabling your adblocker.