Solve the System of Equations y=5/3x y=2x-1

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

Eliminate the equal sides of each equation and combine.

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

Solve $\frac{5}{3} x = 2 x - 1$ for $x$ .

Simplify $\frac{5}{3} x$ .

Rewrite.

$0 + 0 + \frac{5}{3} x = 2 x - 1$

Simplify by adding zeros.

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

Combine $\frac{5}{3}$ and $x$ .

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

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $5 x - 2 x \cdot 3$ .

Factor $x$ out of $5 x$ .

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

Factor $x$ out of $- 2 x \cdot 3$ .

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

Factor $x$ out of $x \cdot 5 + x (- 2 \cdot 3)$ .

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

Multiply $- 2$ by $3$ .

$\frac{x (5 - 6)}{3} = - 1$

Subtract $6$ from $5$ .

$\frac{x \cdot - 1}{3} = - 1$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{3} = - 1$

Move the negative in front of the fraction.

$- \frac{x}{3} = - 1$

Multiply both sides of the equation by $- 3$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 3 \frac{- x}{3} = - 3 \cdot - 1$

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 \cdot - 1$

Rewrite the expression.

$- - x = - 3 \cdot - 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot - 1$

Multiply $x$ by $1$ .

$x = - 3 \cdot - 1$

Simplify the right side.

Multiply $- 3$ by $- 1$ .

$x = 3$

Evaluate $y$ when $x = 3$ .

Substitute $3$ for $x$ .

$y = 2 (3) - 1$

Simplify $2 (3) - 1$ .

Multiply $2$ by $3$ .

$y = 6 - 1$

Subtract $1$ from $6$ .

$y = 5$

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

$(3, 5)$

The result can be shown in multiple forms.

Point Form:

$(3, 5)$

Equation Form:

$x = 3, y = 5$

Solve the System of Equations y=5/3x y=2x-1

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