Solve by Addition/Elimination 3/4x+5/2y=8 , 1/8x-3/4y=-1

$\frac{3}{4} x + \frac{5}{2} y = 8$ , $\frac{1}{8} x - \frac{3}{4} y = - 1$

Step 1

Multiply each term in $\frac{3}{4} x + \frac{5}{2} y = 8$ by $4$ to eliminate the fractions.

Multiply each term in $\frac{3}{4} x + \frac{5}{2} y = 8$ by $4$ .

$\frac{3}{4} x \cdot 4 + \frac{5}{2} y \cdot 4 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Simplify the left side.

Simplify each term.

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} \cdot 4 + \frac{5}{2} y \cdot 4 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 x}{4} \cdot 4 + \frac{5}{2} y \cdot 4 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Rewrite the expression.

$3 x + \frac{5}{2} y \cdot 4 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

$3 x + \frac{5}{2} y \cdot 4 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Combine $\frac{5}{2}$ and $y$ .

$3 x + \frac{5 y}{2} \cdot 4 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$3 x + \frac{5 y}{2} \cdot (2 (2)) = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Cancel the common factor.

$3 x + \frac{5 y}{2} \cdot (2 \cdot 2) = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Rewrite the expression.

$3 x + 5 y \cdot 2 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

$3 x + 5 y \cdot 2 = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Multiply $2$ by $5$ .

$3 x + 10 y = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

$3 x + 10 y = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

$3 x + 10 y = 8 \cdot 4$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Simplify the right side.

Multiply $8$ by $4$ .

$3 x + 10 y = 32$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

$3 x + 10 y = 32$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

$3 x + 10 y = 32$

$\frac{1}{8} x - \frac{3}{4} y = - 1$

Step 2

Multiply each term in $\frac{1}{8} x - \frac{3}{4} y = - 1$ by $8$ to eliminate the fractions.

Multiply each term in $\frac{1}{8} x - \frac{3}{4} y = - 1$ by $8$ .

$\frac{1}{8} x \cdot 8 - \frac{3}{4} y \cdot 8 = - 1 \cdot 8$

$3 x + 10 y = 32$

Simplify the left side.

Simplify each term.

Combine $\frac{1}{8}$ and $x$ .

$\frac{x}{8} \cdot 8 - \frac{3}{4} y \cdot 8 = - 1 \cdot 8$

$3 x + 10 y = 32$

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{x}{8} \cdot 8 - \frac{3}{4} y \cdot 8 = - 1 \cdot 8$

$3 x + 10 y = 32$

Rewrite the expression.

$x - \frac{3}{4} y \cdot 8 = - 1 \cdot 8$

$3 x + 10 y = 32$

$x - \frac{3}{4} y \cdot 8 = - 1 \cdot 8$

$3 x + 10 y = 32$

Combine $y$ and $\frac{3}{4}$ .

$x - \frac{y \cdot 3}{4} \cdot 8 = - 1 \cdot 8$

$3 x + 10 y = 32$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{y \cdot 3}{4}$ into the numerator.

$x + \frac{- y \cdot 3}{4} \cdot 8 = - 1 \cdot 8$

$3 x + 10 y = 32$

Factor $4$ out of $8$ .

$x + \frac{- y \cdot 3}{4} \cdot (4 (2)) = - 1 \cdot 8$

$3 x + 10 y = 32$

Cancel the common factor.

$x + \frac{- y \cdot 3}{4} \cdot (4 \cdot 2) = - 1 \cdot 8$

$3 x + 10 y = 32$

Rewrite the expression.

$x - y \cdot 3 \cdot 2 = - 1 \cdot 8$

$3 x + 10 y = 32$

$x - y \cdot 3 \cdot 2 = - 1 \cdot 8$

$3 x + 10 y = 32$

Multiply $3$ by $- 1$ .

$x - 3 y \cdot 2 = - 1 \cdot 8$

$3 x + 10 y = 32$

Multiply $2$ by $- 3$ .

$x - 6 y = - 1 \cdot 8$

$3 x + 10 y = 32$

$x - 6 y = - 1 \cdot 8$

$3 x + 10 y = 32$

$x - 6 y = - 1 \cdot 8$

$3 x + 10 y = 32$

Simplify the right side.

Multiply $- 1$ by $8$ .

$x - 6 y = - 8$

$3 x + 10 y = 32$

$x - 6 y = - 8$

$3 x + 10 y = 32$

$x - 6 y = - 8$

$3 x + 10 y = 32$

Step 3

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

$3 x + 10 y = 32$

$(- 3) \cdot (x - 6 y) = (- 3) (- 8)$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (x - 6 y)$ .

Apply the distributive property.

$3 x + 10 y = 32$

$- 3 x - 3 (- 6 y) = (- 3) (- 8)$

Multiply $- 6$ by $- 3$ .

$3 x + 10 y = 32$

$- 3 x + 18 y = (- 3) (- 8)$

$3 x + 10 y = 32$

$- 3 x + 18 y = (- 3) (- 8)$

$3 x + 10 y = 32$

$- 3 x + 18 y = (- 3) (- 8)$

Simplify the right side.

Multiply $- 3$ by $- 8$ .

$3 x + 10 y = 32$

$- 3 x + 18 y = 24$

$3 x + 10 y = 32$

$- 3 x + 18 y = 24$

$3 x + 10 y = 32$

$- 3 x + 18 y = 24$

Step 5

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

				$3$	$x$	$+$	$1$	$0$	$y$	$=$	$3$	$2$
$+$			$-$	$3$	$x$	$+$	$1$	$8$	$y$	$=$	$2$	$4$
							$2$	$8$	$y$	$=$	$5$	$6$

Step 6

Divide each term in $28 y = 56$ by $28$ and simplify.

Divide each term in $28 y = 56$ by $28$ .

$\frac{28 y}{28} = \frac{56}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 y}{28} = \frac{56}{28}$

Divide $y$ by $1$ .

$y = \frac{56}{28}$

$y = \frac{56}{28}$

$y = \frac{56}{28}$

Simplify the right side.

Divide $56$ by $28$ .

$y = 2$

$y = 2$

$y = 2$

Step 7

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 $x$ .

$3 x + 10 (2) = 32$

Multiply $10$ by $2$ .

$3 x + 20 = 32$

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

Subtract $20$ from both sides of the equation.

$3 x = 32 - 20$

Subtract $20$ from $32$ .

$3 x = 12$

$3 x = 12$

Divide each term in $3 x = 12$ by $3$ and simplify.

Divide each term in $3 x = 12$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3}$

Divide $x$ by $1$ .

$x = \frac{12}{3}$

$x = \frac{12}{3}$

$x = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x = 4$

$x = 4$

$x = 4$

$x = 4$

Step 8

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

$(4, 2)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Step 10

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