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

$2 x - 1 = y$ $3 x - 1 = y$

Step 1

Rewrite the equation as $y = 2 x - 1$ .

$y = 2 x - 1$

$3 x - 1 = y$

Step 2

Replace all occurrences of $y$ with $2 x - 1$ in each equation.

Replace all occurrences of $y$ in $3 x - 1 = y$ with $2 x - 1$ .

$3 x - 1 = 2 x - 1$

$y = 2 x - 1$

Simplify the left side.

Remove parentheses.

$3 x - 1 = 2 x - 1$

$y = 2 x - 1$

$3 x - 1 = 2 x - 1$

$y = 2 x - 1$

$3 x - 1 = 2 x - 1$

$y = 2 x - 1$

Step 3

Solve for $x$ in $3 x - 1 = 2 x - 1$ .

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

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

$3 x - 1 - 2 x = - 1$

$y = 2 x - 1$

Subtract $2 x$ from $3 x$ .

$x - 1 = - 1$

$y = 2 x - 1$

$x - 1 = - 1$

$y = 2 x - 1$

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

Add $1$ to both sides of the equation.

$x = - 1 + 1$

$y = 2 x - 1$

Add $- 1$ and $1$ .

$x = 0$

$y = 2 x - 1$

$x = 0$

$y = 2 x - 1$

$x = 0$

$y = 2 x - 1$

Step 4

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $y = 2 x - 1$ with $0$ .

$y = 2 (0) - 1$

$x = 0$

Simplify the right side.

Simplify $2 (0) - 1$ .

Multiply $2$ by $0$ .

$y = 0 - 1$

$x = 0$

Subtract $1$ from $0$ .

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

Step 5

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

$(0, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 1)$

Equation Form:

$x = 0, y = - 1$

Step 7

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

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