Solve the System of Equations 2y=x-4 4x+3y=5

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

Step 1

Divide each term in $2 y = x - 4$ by $2$ and simplify.

Divide each term in $2 y = x - 4$ by $2$ .

$\frac{2 y}{2} = \frac{x}{2} + \frac{- 4}{2}$

$4 x + 3 y = 5$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{x}{2} + \frac{- 4}{2}$

$4 x + 3 y = 5$

Divide $y$ by $1$ .

$y = \frac{x}{2} + \frac{- 4}{2}$

$4 x + 3 y = 5$

$y = \frac{x}{2} + \frac{- 4}{2}$

$4 x + 3 y = 5$

$y = \frac{x}{2} + \frac{- 4}{2}$

$4 x + 3 y = 5$

Simplify the right side.

Divide $- 4$ by $2$ .

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

$4 x + 3 y = 5$

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

$4 x + 3 y = 5$

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

$4 x + 3 y = 5$

Step 2

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

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

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

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

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

Combine $3$ and $\frac{x}{2}$ .

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

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

Multiply $3$ by $- 2$ .

$4 x + \frac{3 x}{2} - 6 = 5$

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

$4 x + \frac{3 x}{2} - 6 = 5$

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

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 x \cdot \frac{2}{2} + \frac{3 x}{2} - 6 = 5$

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

Simplify terms.

Combine $4 x$ and $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{2} + \frac{3 x}{2} - 6 = 5$

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

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 + 3 x}{2} - 6 = 5$

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

$\frac{4 x \cdot 2 + 3 x}{2} - 6 = 5$

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $4 x \cdot 2 + 3 x$ .

Factor $x$ out of $4 x \cdot 2$ .

$\frac{x (4 \cdot 2) + 3 x}{2} - 6 = 5$

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

Factor $x$ out of $3 x$ .

$\frac{x (4 \cdot 2) + x \cdot 3}{2} - 6 = 5$

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

Factor $x$ out of $x (4 \cdot 2) + x \cdot 3$ .

$\frac{x (4 \cdot 2 + 3)}{2} - 6 = 5$

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

$\frac{x (4 \cdot 2 + 3)}{2} - 6 = 5$

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

Multiply $4$ by $2$ .

$\frac{x (8 + 3)}{2} - 6 = 5$

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

Add $8$ and $3$ .

$\frac{x \cdot 11}{2} - 6 = 5$

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

$\frac{x \cdot 11}{2} - 6 = 5$

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

Move $11$ to the left of $x$ .

$\frac{11 x}{2} - 6 = 5$

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

$\frac{11 x}{2} - 6 = 5$

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

$\frac{11 x}{2} - 6 = 5$

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

$\frac{11 x}{2} - 6 = 5$

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

$\frac{11 x}{2} - 6 = 5$

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

Step 3

Solve for $x$ in $\frac{11 x}{2} - 6 = 5$ .

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

Add $6$ to both sides of the equation.

$\frac{11 x}{2} = 5 + 6$

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

Add $5$ and $6$ .

$\frac{11 x}{2} = 11$

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

$\frac{11 x}{2} = 11$

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

Multiply both sides of the equation by $\frac{2}{11}$ .

$\frac{2}{11} \cdot \frac{11 x}{2} = \frac{2}{11} \cdot 11$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{11} \cdot \frac{11 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{11} \cdot \frac{11 x}{2} = \frac{2}{11} \cdot 11$

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

Rewrite the expression.

$\frac{1}{11} \cdot (11 x) = \frac{2}{11} \cdot 11$

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

$\frac{1}{11} \cdot (11 x) = \frac{2}{11} \cdot 11$

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

Cancel the common factor of $11$ .

Factor $11$ out of $11 x$ .

$\frac{1}{11} \cdot (11 (x)) = \frac{2}{11} \cdot 11$

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

Cancel the common factor.

$\frac{1}{11} \cdot (11 x) = \frac{2}{11} \cdot 11$

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

Rewrite the expression.

$x = \frac{2}{11} \cdot 11$

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

$x = \frac{2}{11} \cdot 11$

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

$x = \frac{2}{11} \cdot 11$

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

$x = \frac{2}{11} \cdot 11$

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

Simplify the right side.

Cancel the common factor of $11$ .

Cancel the common factor.

$x = \frac{2}{11} \cdot 11$

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

Rewrite the expression.

$x = 2$

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

$x = 2$

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

$x = 2$

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

$x = 2$

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

$x = 2$

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

Step 4

Replace all occurrences of $x$ with $2$ in each equation.

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

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

$x = 2$

Simplify the right side.

Simplify $\frac{2}{2} - 2$ .

Divide $2$ by $2$ .

$y = 1 - 2$

$x = 2$

Subtract $2$ from $1$ .

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

Step 5

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

$(2, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 7

Solve the System of Equations 2y=x-4 4x+3y=5

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