Solve the System of Equations 6x=4y-42 4x+y=5

$6 x = 4 y - 42$ $4 x + y = 5$

Step 1

Divide each term in $6 x = 4 y - 42$ by $6$ and simplify.

Divide each term in $6 x = 4 y - 42$ by $6$ .

$\frac{6 x}{6} = \frac{4 y}{6} + \frac{- 42}{6}$

$4 x + y = 5$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{4 y}{6} + \frac{- 42}{6}$

$4 x + y = 5$

Divide $x$ by $1$ .

$x = \frac{4 y}{6} + \frac{- 42}{6}$

$4 x + y = 5$

$x = \frac{4 y}{6} + \frac{- 42}{6}$

$4 x + y = 5$

$x = \frac{4 y}{6} + \frac{- 42}{6}$

$4 x + y = 5$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 y$ .

$x = \frac{2 (2 y)}{6} + \frac{- 42}{6}$

$4 x + y = 5$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 (2 y)}{2 (3)} + \frac{- 42}{6}$

$4 x + y = 5$

Cancel the common factor.

$x = \frac{2 (2 y)}{2 \cdot 3} + \frac{- 42}{6}$

$4 x + y = 5$

Rewrite the expression.

$x = \frac{2 y}{3} + \frac{- 42}{6}$

$4 x + y = 5$

$x = \frac{2 y}{3} + \frac{- 42}{6}$

$4 x + y = 5$

$x = \frac{2 y}{3} + \frac{- 42}{6}$

$4 x + y = 5$

Divide $- 42$ by $6$ .

$x = \frac{2 y}{3} - 7$

$4 x + y = 5$

$x = \frac{2 y}{3} - 7$

$4 x + y = 5$

$x = \frac{2 y}{3} - 7$

$4 x + y = 5$

$x = \frac{2 y}{3} - 7$

$4 x + y = 5$

Step 2

Replace all occurrences of $x$ with $\frac{2 y}{3} - 7$ in each equation.

Replace all occurrences of $x$ in $4 x + y = 5$ with $\frac{2 y}{3} - 7$ .

$4 (\frac{2 y}{3} - 7) + y = 5$

$x = \frac{2 y}{3} - 7$

Simplify the left side.

Simplify $4 (\frac{2 y}{3} - 7) + y$ .

Simplify each term.

Apply the distributive property.

$4 (\frac{2 y}{3}) + 4 \cdot - 7 + y = 5$

$x = \frac{2 y}{3} - 7$

Multiply $4 \frac{2 y}{3}$ .

Combine $4$ and $\frac{2 y}{3}$ .

$\frac{4 (2 y)}{3} + 4 \cdot - 7 + y = 5$

$x = \frac{2 y}{3} - 7$

Multiply $2$ by $4$ .

$\frac{8 y}{3} + 4 \cdot - 7 + y = 5$

$x = \frac{2 y}{3} - 7$

$\frac{8 y}{3} + 4 \cdot - 7 + y = 5$

$x = \frac{2 y}{3} - 7$

Multiply $4$ by $- 7$ .

$\frac{8 y}{3} - 28 + y = 5$

$x = \frac{2 y}{3} - 7$

$\frac{8 y}{3} - 28 + y = 5$

$x = \frac{2 y}{3} - 7$

To write $y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8 y}{3} + y \cdot \frac{3}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

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

$\frac{8 y}{3} + \frac{y \cdot 3}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

Combine the numerators over the common denominator.

$\frac{8 y + y \cdot 3}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

Add $8 y$ and $y \cdot 3$ .

Reorder $y$ and $3$ .

$\frac{8 y + 3 \cdot y}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

Add $8 y$ and $3 \cdot y$ .

$\frac{11 y}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

$\frac{11 y}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

$\frac{11 y}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

$\frac{11 y}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

$\frac{11 y}{3} - 28 = 5$

$x = \frac{2 y}{3} - 7$

Step 3

Solve for $y$ in $\frac{11 y}{3} - 28 = 5$ .

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

Add $28$ to both sides of the equation.

$\frac{11 y}{3} = 5 + 28$

$x = \frac{2 y}{3} - 7$

Add $5$ and $28$ .

$\frac{11 y}{3} = 33$

$x = \frac{2 y}{3} - 7$

$\frac{11 y}{3} = 33$

$x = \frac{2 y}{3} - 7$

Multiply both sides of the equation by $\frac{3}{11}$ .

$\frac{3}{11} \cdot \frac{11 y}{3} = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{11} \cdot \frac{11 y}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{11} \cdot \frac{11 y}{3} = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

Rewrite the expression.

$\frac{1}{11} \cdot (11 y) = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

$\frac{1}{11} \cdot (11 y) = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

Cancel the common factor of $11$ .

Factor $11$ out of $11 y$ .

$\frac{1}{11} \cdot (11 (y)) = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

Cancel the common factor.

$\frac{1}{11} \cdot (11 y) = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

Rewrite the expression.

$y = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

$y = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

$y = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

$y = \frac{3}{11} \cdot 33$

$x = \frac{2 y}{3} - 7$

Simplify the right side.

Simplify $\frac{3}{11} \cdot 33$ .

Cancel the common factor of $11$ .

Factor $11$ out of $33$ .

$y = \frac{3}{11} \cdot (11 (3))$

$x = \frac{2 y}{3} - 7$

Cancel the common factor.

$y = \frac{3}{11} \cdot (11 \cdot 3)$

$x = \frac{2 y}{3} - 7$

Rewrite the expression.

$y = 3 \cdot 3$

$x = \frac{2 y}{3} - 7$

$y = 3 \cdot 3$

$x = \frac{2 y}{3} - 7$

Multiply $3$ by $3$ .

$y = 9$

$x = \frac{2 y}{3} - 7$

$y = 9$

$x = \frac{2 y}{3} - 7$

$y = 9$

$x = \frac{2 y}{3} - 7$

$y = 9$

$x = \frac{2 y}{3} - 7$

$y = 9$

$x = \frac{2 y}{3} - 7$

Step 4

Replace all occurrences of $y$ with $9$ in each equation.

Replace all occurrences of $y$ in $x = \frac{2 y}{3} - 7$ with $9$ .

$x = \frac{2 (9)}{3} - 7$

$y = 9$

Simplify the right side.

Simplify $\frac{2 (9)}{3} - 7$ .

Multiply $2$ by $9$ .

$x = \frac{18}{3} - 7$

$y = 9$

Divide $18$ by $3$ .

$x = 6 - 7$

$y = 9$

Subtract $7$ from $6$ .

$x = - 1$

$y = 9$

$x = - 1$

$y = 9$

$x = - 1$

$y = 9$

$x = - 1$

$y = 9$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 1, 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, 9)$

Equation Form:

$x = - 1, y = 9$

Step 7

Solve the System of Equations 6x=4y-42 4x+y=5

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