Solve by Addition/Elimination 4x-2y=9 , 12x-7y=6

$4 x - 2 y = 9$ , $12 x - 7 y = 6$

Step 1

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

$(- 3) \cdot (4 x - 2 y) = (- 3) (9)$

$12 x - 7 y = 6$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 3 (4 x) - 3 (- 2 y) = (- 3) (9)$

$12 x - 7 y = 6$

Multiply.

Multiply $4$ by $- 3$ .

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

$12 x - 7 y = 6$

Multiply $- 2$ by $- 3$ .

$- 12 x + 6 y = (- 3) (9)$

$12 x - 7 y = 6$

$- 12 x + 6 y = (- 3) (9)$

$12 x - 7 y = 6$

$- 12 x + 6 y = (- 3) (9)$

$12 x - 7 y = 6$

$- 12 x + 6 y = (- 3) (9)$

$12 x - 7 y = 6$

Simplify the right side.

Multiply $- 3$ by $9$ .

$- 12 x + 6 y = - 27$

$12 x - 7 y = 6$

$- 12 x + 6 y = - 27$

$12 x - 7 y = 6$

$- 12 x + 6 y = - 27$

$12 x - 7 y = 6$

Step 3

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

	$-$	$1$	$2$	$x$	$+$	$6$	$y$	$=$	$-$	$2$	$7$
$+$		$1$	$2$	$x$	$-$	$7$	$y$	$=$			$6$
						$-$	$y$	$=$	$-$	$2$	$1$

Step 4

Divide each term in $- y = - 21$ by $- 1$ and simplify.

Divide each term in $- y = - 21$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 21}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 21}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 21}{- 1}$

Simplify the right side.

Divide $- 21$ by $- 1$ .

$y = 21$

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 $x$ .

$- 12 x + 6 (21) = - 27$

Multiply $6$ by $21$ .

$- 12 x + 126 = - 27$

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

Subtract $126$ from both sides of the equation.

$- 12 x = - 27 - 126$

Subtract $126$ from $- 27$ .

$- 12 x = - 153$

Divide each term in $- 12 x = - 153$ by $- 12$ and simplify.

Divide each term in $- 12 x = - 153$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 153}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 153}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 153}{- 12}$

Simplify the right side.

Cancel the common factor of $- 153$ and $- 12$ .

Factor $- 3$ out of $- 153$ .

$x = \frac{- 3 (51)}{- 12}$

Cancel the common factors.

Factor $- 3$ out of $- 12$ .

$x = \frac{- 3 \cdot 51}{- 3 \cdot 4}$

Cancel the common factor.

$x = \frac{- 3 \cdot 51}{- 3 \cdot 4}$

Rewrite the expression.

$x = \frac{51}{4}$

Step 6

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

$(\frac{51}{4}, 21)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(\frac{51}{4}, 21)$

Equation Form:

$x = \frac{51}{4}, y = 21$

Step 8

Solve by Addition/Elimination 4x-2y=9 , 12x-7y=6

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