Solve by Addition/Elimination 4x-7y=3 x-7y=-15

$4 x - 7 y = 3$ $x - 7 y = - 15$

Step 1

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

$4 x - 7 y = 3$

$(- 4) \cdot (x - 7 y) = (- 4) (- 15)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (x - 7 y)$ .

Apply the distributive property.

$4 x - 7 y = 3$

$- 4 x - 4 (- 7 y) = (- 4) (- 15)$

Multiply $- 7$ by $- 4$ .

$4 x - 7 y = 3$

$- 4 x + 28 y = (- 4) (- 15)$

$4 x - 7 y = 3$

$- 4 x + 28 y = (- 4) (- 15)$

$4 x - 7 y = 3$

$- 4 x + 28 y = (- 4) (- 15)$

Simplify the right side.

Multiply $- 4$ by $- 15$ .

$4 x - 7 y = 3$

$- 4 x + 28 y = 60$

$4 x - 7 y = 3$

$- 4 x + 28 y = 60$

$4 x - 7 y = 3$

$- 4 x + 28 y = 60$

Step 3

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

		$4$	$x$		$-$	$7$	$y$	$=$		$3$
$+$	$-$	$4$	$x$	$+$	$2$	$8$	$y$	$=$	$6$	$0$
					$2$	$1$	$y$	$=$	$6$	$3$

Step 4

Divide each term in $21 y = 63$ by $21$ and simplify.

Divide each term in $21 y = 63$ by $21$ .

$\frac{21 y}{21} = \frac{63}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 y}{21} = \frac{63}{21}$

Divide $y$ by $1$ .

$y = \frac{63}{21}$

Simplify the right side.

Divide $63$ by $21$ .

$y = 3$

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 $x$ .

$4 x - 7 \cdot 3 = 3$

Multiply $- 7$ by $3$ .

$4 x - 21 = 3$

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

Add $21$ to both sides of the equation.

$4 x = 3 + 21$

Add $3$ and $21$ .

$4 x = 24$

Divide each term in $4 x = 24$ by $4$ and simplify.

Divide each term in $4 x = 24$ by $4$ .

$\frac{4 x}{4} = \frac{24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{24}{4}$

Divide $x$ by $1$ .

$x = \frac{24}{4}$

Simplify the right side.

Divide $24$ by $4$ .

$x = 6$

Step 6

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

$(6, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(6, 3)$

Equation Form:

$x = 6, y = 3$

Step 8

Solve by Addition/Elimination 4x-7y=3 x-7y=-15

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