Solve by Addition/Elimination 4y=3x+5 6y=3x+21

$4 y = 3 x + 5$ $6 y = 3 x + 21$

Step 1

Move all terms containing variables to the left.

Subtract $3 x$ from both sides of the equation.

$4 y - 3 x = 5, 6 y = 3 x + 21$

Subtract $3 x$ from both sides of the equation.

$4 y - 3 x = 5, 6 y - 3 x = 21$

Step 2

Reorder the polynomial.

$- 3 x + 4 y = 5$

$6 y - 3 x = 21$

Step 3

Reorder the polynomial.

$- 3 x + 6 y = 21$

$- 3 x + 4 y = 5$

Step 4

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

$(- 1) \cdot (- 3 x + 4 y) = (- 1) (5)$

$- 3 x + 6 y = 21$

Step 5

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (- 3 x + 4 y)$ .

Apply the distributive property.

$- 1 (- 3 x) - 1 (4 y) = (- 1) (5)$

$- 3 x + 6 y = 21$

Multiply.

Multiply $- 3$ by $- 1$ .

$3 x - 1 (4 y) = (- 1) (5)$

$- 3 x + 6 y = 21$

Multiply $4$ by $- 1$ .

$3 x - 4 y = (- 1) (5)$

$- 3 x + 6 y = 21$

$3 x - 4 y = (- 1) (5)$

$- 3 x + 6 y = 21$

$3 x - 4 y = (- 1) (5)$

$- 3 x + 6 y = 21$

$3 x - 4 y = (- 1) (5)$

$- 3 x + 6 y = 21$

Simplify the right side.

Multiply $- 1$ by $5$ .

$3 x - 4 y = - 5$

$- 3 x + 6 y = 21$

$3 x - 4 y = - 5$

$- 3 x + 6 y = 21$

$3 x - 4 y = - 5$

$- 3 x + 6 y = 21$

Step 6

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

		$3$	$x$	$-$	$4$	$y$	$=$	$-$	$5$
$+$	$-$	$3$	$x$	$+$	$6$	$y$	$=$	$2$	$1$
					$2$	$y$	$=$	$1$	$6$

Step 7

Divide each term in $2 y = 16$ by $2$ and simplify.

Divide each term in $2 y = 16$ by $2$ .

$\frac{2 y}{2} = \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{16}{2}$

Divide $y$ by $1$ .

$y = \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

$y = 8$

Step 8

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 $x$ .

$3 x - 4 \cdot 8 = - 5$

Multiply $- 4$ by $8$ .

$3 x - 32 = - 5$

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

Add $32$ to both sides of the equation.

$3 x = - 5 + 32$

Add $- 5$ and $32$ .

$3 x = 27$

Divide each term in $3 x = 27$ by $3$ and simplify.

Divide each term in $3 x = 27$ by $3$ .

$\frac{3 x}{3} = \frac{27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{27}{3}$

Divide $x$ by $1$ .

$x = \frac{27}{3}$

Simplify the right side.

Divide $27$ by $3$ .

$x = 9$

Step 9

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

$(9, 8)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(9, 8)$

Equation Form:

$x = 9, y = 8$

Step 11

Solve by Addition/Elimination 4y=3x+5 6y=3x+21

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