Solve by Substitution 4x-y=3 , 7x-9y=-2

$4 x - y = 3$ , $7 x - 9 y = - 2$

Step 1

Solve for $x$ in $4 x - y = 3$ .

Add $y$ to both sides of the equation.

$4 x = 3 + y$

$7 x - 9 y = - 2$

Divide each term in $4 x = 3 + y$ by $4$ and simplify.

Divide each term in $4 x = 3 + y$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4} + \frac{y}{4}$

$7 x - 9 y = - 2$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4} + \frac{y}{4}$

$7 x - 9 y = - 2$

Divide $x$ by $1$ .

$x = \frac{3}{4} + \frac{y}{4}$

$7 x - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$7 x - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$7 x - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$7 x - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$7 x - 9 y = - 2$

Step 2

Replace all occurrences of $x$ with $\frac{3}{4} + \frac{y}{4}$ in each equation.

Replace all occurrences of $x$ in $7 x - 9 y = - 2$ with $\frac{3}{4} + \frac{y}{4}$ .

$7 (\frac{3}{4} + \frac{y}{4}) - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Simplify the left side.

Simplify $7 (\frac{3}{4} + \frac{y}{4}) - 9 y$ .

Simplify each term.

Apply the distributive property.

$7 (\frac{3}{4}) + 7 (\frac{y}{4}) - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Multiply $7 (\frac{3}{4})$ .

Combine $7$ and $\frac{3}{4}$ .

$\frac{7 \cdot 3}{4} + 7 (\frac{y}{4}) - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Multiply $7$ by $3$ .

$\frac{21}{4} + 7 (\frac{y}{4}) - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$\frac{21}{4} + 7 (\frac{y}{4}) - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Combine $7$ and $\frac{y}{4}$ .

$\frac{21}{4} + \frac{7 y}{4} - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$\frac{21}{4} + \frac{7 y}{4} - 9 y = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

To write $- 9 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{21}{4} + \frac{7 y}{4} - 9 y \cdot \frac{4}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Combine $- 9 y$ and $\frac{4}{4}$ .

$\frac{21}{4} + \frac{7 y}{4} + \frac{- 9 y \cdot 4}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Combine the numerators over the common denominator.

$\frac{21}{4} + \frac{7 y - 9 y \cdot 4}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Combine the numerators over the common denominator.

$\frac{21 + 7 y - 9 y \cdot 4}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Multiply $4$ by $- 9$ .

$\frac{21 + 7 y - 36 y}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Subtract $36 y$ from $7 y$ .

$\frac{21 - 29 y}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$\frac{21 - 29 y}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$\frac{21 - 29 y}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

$\frac{21 - 29 y}{4} = - 2$

$x = \frac{3}{4} + \frac{y}{4}$

Step 3

Solve for $y$ in $\frac{21 - 29 y}{4} = - 2$ .

Multiply both sides by $4$ .

$\frac{21 - 29 y}{4} \cdot 4 = - 2 \cdot 4$

$x = \frac{3}{4} + \frac{y}{4}$

Simplify.

Simplify the left side.

Simplify $\frac{21 - 29 y}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{21 - 29 y}{4} \cdot 4 = - 2 \cdot 4$

$x = \frac{3}{4} + \frac{y}{4}$

Rewrite the expression.

$21 - 29 y = - 2 \cdot 4$

$x = \frac{3}{4} + \frac{y}{4}$

$21 - 29 y = - 2 \cdot 4$

$x = \frac{3}{4} + \frac{y}{4}$

Reorder $21$ and $- 29 y$ .

$- 29 y + 21 = - 2 \cdot 4$

$x = \frac{3}{4} + \frac{y}{4}$

$- 29 y + 21 = - 2 \cdot 4$

$x = \frac{3}{4} + \frac{y}{4}$

$- 29 y + 21 = - 2 \cdot 4$

$x = \frac{3}{4} + \frac{y}{4}$

Simplify the right side.

Multiply $- 2$ by $4$ .

$- 29 y + 21 = - 8$

$x = \frac{3}{4} + \frac{y}{4}$

$- 29 y + 21 = - 8$

$x = \frac{3}{4} + \frac{y}{4}$

$- 29 y + 21 = - 8$

$x = \frac{3}{4} + \frac{y}{4}$

Solve for $y$ .

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

Subtract $21$ from both sides of the equation.

$- 29 y = - 8 - 21$

$x = \frac{3}{4} + \frac{y}{4}$

Subtract $21$ from $- 8$ .

$- 29 y = - 29$

$x = \frac{3}{4} + \frac{y}{4}$

$- 29 y = - 29$

$x = \frac{3}{4} + \frac{y}{4}$

Divide each term in $- 29 y = - 29$ by $- 29$ and simplify.

Divide each term in $- 29 y = - 29$ by $- 29$ .

$\frac{- 29 y}{- 29} = \frac{- 29}{- 29}$

$x = \frac{3}{4} + \frac{y}{4}$

Simplify the left side.

Cancel the common factor of $- 29$ .

Cancel the common factor.

$\frac{- 29 y}{- 29} = \frac{- 29}{- 29}$

$x = \frac{3}{4} + \frac{y}{4}$

Divide $y$ by $1$ .

$y = \frac{- 29}{- 29}$

$x = \frac{3}{4} + \frac{y}{4}$

$y = \frac{- 29}{- 29}$

$x = \frac{3}{4} + \frac{y}{4}$

$y = \frac{- 29}{- 29}$

$x = \frac{3}{4} + \frac{y}{4}$

Simplify the right side.

Divide $- 29$ by $- 29$ .

$y = 1$

$x = \frac{3}{4} + \frac{y}{4}$

$y = 1$

$x = \frac{3}{4} + \frac{y}{4}$

$y = 1$

$x = \frac{3}{4} + \frac{y}{4}$

$y = 1$

$x = \frac{3}{4} + \frac{y}{4}$

$y = 1$

$x = \frac{3}{4} + \frac{y}{4}$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

Replace all occurrences of $y$ in $x = \frac{3}{4} + \frac{y}{4}$ with $1$ .

$x = \frac{3}{4} + \frac{1}{4}$

$y = 1$

Simplify the right side.

Simplify $\frac{3}{4} + \frac{1}{4}$ .

Combine the numerators over the common denominator.

$x = \frac{3 + 1}{4}$

$y = 1$

Simplify the expression.

Add $3$ and $1$ .

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

$y = 1$

Divide $4$ by $4$ .

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

Step 5

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

$(1, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 7

Solve by Substitution 4x-y=3 , 7x-9y=-2

Related Questions

Support LCMGCF.com by disabling your adblocker.