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

$y = 2$ and $y = 2 x - 3$

Step 1

Eliminate the equal sides of each equation and combine.

$2 = 2 x - 3$

Step 2

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

Rewrite the equation as $2 x - 3 = 2$ .

$2 x - 3 = 2$

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

Add $3$ to both sides of the equation.

$2 x = 2 + 3$

Add $2$ and $3$ .

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Step 3

Evaluate $y$ when $x = \frac{5}{2}$ .

Substitute $\frac{5}{2}$ for $x$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 5 - 3$

Subtract $3$ from $5$ .

$y = 2$

Step 4

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

$(\frac{5}{2}, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{5}{2}, 2)$

Equation Form:

$x = \frac{5}{2}, y = 2$

Step 6