Solve by Substitution 4y=5x-1 , 3x-2y=1

$4 y = 5 x - 1$ , $3 x - 2 y = 1$

Step 1

Divide each term in $4 y = 5 x - 1$ by $4$ and simplify.

Divide each term in $4 y = 5 x - 1$ by $4$ .

$\frac{4 y}{4} = \frac{5 x}{4} + \frac{- 1}{4}$

$3 x - 2 y = 1$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{5 x}{4} + \frac{- 1}{4}$

$3 x - 2 y = 1$

Divide $y$ by $1$ .

$y = \frac{5 x}{4} + \frac{- 1}{4}$

$3 x - 2 y = 1$

$y = \frac{5 x}{4} + \frac{- 1}{4}$

$3 x - 2 y = 1$

$y = \frac{5 x}{4} + \frac{- 1}{4}$

$3 x - 2 y = 1$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - 2 y = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - 2 y = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - 2 y = 1$

Step 2

Replace all occurrences of $y$ with $\frac{5 x}{4} - \frac{1}{4}$ in each equation.

Replace all occurrences of $y$ in $3 x - 2 y = 1$ with $\frac{5 x}{4} - \frac{1}{4}$ .

$3 x - 2 (\frac{5 x}{4} - \frac{1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Simplify the left side.

Simplify $3 x - 2 (\frac{5 x}{4} - \frac{1}{4})$ .

Simplify each term.

Apply the distributive property.

$3 x - 2 \frac{5 x}{4} - 2 (- \frac{1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$3 x + 2 (- 1) (\frac{5 x}{4}) - 2 (- \frac{1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Factor $2$ out of $4$ .

$3 x + 2 \cdot (- 1 \frac{5 x}{2 \cdot 2}) - 2 (- \frac{1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Cancel the common factor.

$3 x + 2 \cdot (- 1 \frac{5 x}{2 \cdot 2}) - 2 (- \frac{1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Rewrite the expression.

$3 x - 1 \frac{5 x}{2} - 2 (- \frac{1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - 1 \frac{5 x}{2} - 2 (- \frac{1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$3 x - 1 \frac{5 x}{2} - 2 (\frac{- 1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Factor $2$ out of $- 2$ .

$3 x - 1 \frac{5 x}{2} + 2 (- 1) (\frac{- 1}{4}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Factor $2$ out of $4$ .

$3 x - 1 \frac{5 x}{2} + 2 \cdot (- 1 \frac{- 1}{2 \cdot 2}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Cancel the common factor.

$3 x - 1 \frac{5 x}{2} + 2 \cdot (- 1 \frac{- 1}{2 \cdot 2}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Rewrite the expression.

$3 x - 1 \frac{5 x}{2} - 1 (\frac{- 1}{2}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - 1 \frac{5 x}{2} - 1 (\frac{- 1}{2}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Simplify each term.

Rewrite $- 1 \frac{5 x}{2}$ as $- \frac{5 x}{2}$ .

$3 x - \frac{5 x}{2} - 1 (\frac{- 1}{2}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Move the negative in front of the fraction.

$3 x - \frac{5 x}{2} - 1 (- \frac{1}{2}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Multiply $- 1 (- \frac{1}{2})$ .

Multiply $- 1$ by $- 1$ .

$3 x - \frac{5 x}{2} + 1 (\frac{1}{2}) = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Multiply $\frac{1}{2}$ by $1$ .

$3 x - \frac{5 x}{2} + \frac{1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - \frac{5 x}{2} + \frac{1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - \frac{5 x}{2} + \frac{1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$3 x - \frac{5 x}{2} + \frac{1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 x \cdot \frac{2}{2} - \frac{5 x}{2} + \frac{1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

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

$\frac{3 x \cdot 2}{2} - \frac{5 x}{2} + \frac{1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - 5 x}{2} + \frac{1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - 5 x + 1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Multiply $2$ by $3$ .

$\frac{6 x - 5 x + 1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Subtract $5 x$ from $6 x$ .

$\frac{x + 1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$\frac{x + 1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$\frac{x + 1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$\frac{x + 1}{2} = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Step 3

Solve for $x$ in $\frac{x + 1}{2} = 1$ .

Multiply both sides of the equation by $2$ .

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

$y = \frac{5 x}{4} - \frac{1}{4}$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$y = \frac{5 x}{4} - \frac{1}{4}$

Rewrite the expression.

$x + 1 = 2 \cdot 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$x + 1 = 2 \cdot 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$x + 1 = 2 \cdot 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Simplify the right side.

Multiply $2$ by $1$ .

$x + 1 = 2$

$y = \frac{5 x}{4} - \frac{1}{4}$

$x + 1 = 2$

$y = \frac{5 x}{4} - \frac{1}{4}$

$x + 1 = 2$

$y = \frac{5 x}{4} - \frac{1}{4}$

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

Subtract $1$ from both sides of the equation.

$x = 2 - 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Subtract $1$ from $2$ .

$x = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$x = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

$x = 1$

$y = \frac{5 x}{4} - \frac{1}{4}$

Step 4

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

Replace all occurrences of $x$ in $y = \frac{5 x}{4} - \frac{1}{4}$ with $1$ .

$y = \frac{5 (1)}{4} - \frac{1}{4}$

$x = 1$

Simplify the right side.

Simplify $\frac{5 (1)}{4} - \frac{1}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{5 (1) - 1}{4}$

$x = 1$

Simplify the expression.

Multiply $5$ by $1$ .

$y = \frac{5 - 1}{4}$

$x = 1$

Subtract $1$ from $5$ .

$y = \frac{4}{4}$

$x = 1$

Divide $4$ by $4$ .

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

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

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