Solve by Addition/Elimination 4x-3y=2 3x+5y=16

$4 x - 3 y = 2$ $3 x + 5 y = 16$

Step 1

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

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

$(4) \cdot (3 x + 5 y) = (4) (16)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$(4) \cdot (3 x + 5 y) = (4) (16)$

Multiply.

Multiply $4$ by $- 3$ .

$- 12 x - 3 (- 3 y) = (- 3) (2)$

$(4) \cdot (3 x + 5 y) = (4) (16)$

Multiply $- 3$ by $- 3$ .

$- 12 x + 9 y = (- 3) (2)$

$(4) \cdot (3 x + 5 y) = (4) (16)$

$- 12 x + 9 y = (- 3) (2)$

$(4) \cdot (3 x + 5 y) = (4) (16)$

$- 12 x + 9 y = (- 3) (2)$

$(4) \cdot (3 x + 5 y) = (4) (16)$

$- 12 x + 9 y = (- 3) (2)$

$(4) \cdot (3 x + 5 y) = (4) (16)$

Simplify the right side.

Multiply $- 3$ by $2$ .

$- 12 x + 9 y = - 6$

$(4) \cdot (3 x + 5 y) = (4) (16)$

$- 12 x + 9 y = - 6$

$(4) \cdot (3 x + 5 y) = (4) (16)$

Simplify the left side.

Simplify $(4) \cdot (3 x + 5 y)$ .

Apply the distributive property.

$- 12 x + 9 y = - 6$

$4 (3 x) + 4 (5 y) = (4) (16)$

Multiply.

Multiply $3$ by $4$ .

$- 12 x + 9 y = - 6$

$12 x + 4 (5 y) = (4) (16)$

Multiply $5$ by $4$ .

$- 12 x + 9 y = - 6$

$12 x + 20 y = (4) (16)$

$- 12 x + 9 y = - 6$

$12 x + 20 y = (4) (16)$

$- 12 x + 9 y = - 6$

$12 x + 20 y = (4) (16)$

$- 12 x + 9 y = - 6$

$12 x + 20 y = (4) (16)$

Simplify the right side.

Multiply $4$ by $16$ .

$- 12 x + 9 y = - 6$

$12 x + 20 y = 64$

$- 12 x + 9 y = - 6$

$12 x + 20 y = 64$

$- 12 x + 9 y = - 6$

$12 x + 20 y = 64$

Step 3

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

	$-$	$1$	$2$	$x$	$+$		$9$	$y$	$=$	$-$	$6$
$+$		$1$	$2$	$x$	$+$	$2$	$0$	$y$	$=$	$6$	$4$
						$2$	$9$	$y$	$=$	$5$	$8$

Step 4

Divide each term in $29 y = 58$ by $29$ and simplify.

Divide each term in $29 y = 58$ by $29$ .

$\frac{29 y}{29} = \frac{58}{29}$

Simplify the left side.

Cancel the common factor of $29$ .

Cancel the common factor.

$\frac{29 y}{29} = \frac{58}{29}$

Divide $y$ by $1$ .

$y = \frac{58}{29}$

Simplify the right side.

Divide $58$ by $29$ .

$y = 2$

Step 5

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 $x$ .

$- 12 x + 9 (2) = - 6$

Multiply $9$ by $2$ .

$- 12 x + 18 = - 6$

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

Subtract $18$ from both sides of the equation.

$- 12 x = - 6 - 18$

Subtract $18$ from $- 6$ .

$- 12 x = - 24$

Divide each term in $- 12 x = - 24$ by $- 12$ and simplify.

Divide each term in $- 12 x = - 24$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 24}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 24}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 12}$

Simplify the right side.

Divide $- 24$ by $- 12$ .

$x = 2$

Step 6

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

$(2, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 2)$

Equation Form:

$x = 2, y = 2$

Step 8

Solve by Addition/Elimination 4x-3y=2 3x+5y=16

Related Questions

Support LCMGCF.com by disabling your adblocker.