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

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

Step 1

Eliminate the equal sides of each equation and combine.

$x = 2 x - 1$

Step 2

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

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

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

$x - 2 x = - 1$

Subtract $2 x$ from $x$ .

$- x = - 1$

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

Divide each term in $- x = - 1$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = 2 (1) - 1$

Simplify $2 (1) - 1$ .

Multiply $2$ by $1$ .

$y = 2 - 1$

Subtract $1$ from $2$ .

$y = 1$

Step 4

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

$(1, 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 6