Solve the System of Equations y=x+1 y=-1/2x+4

$y = x + 1$ $y = - \frac{1}{2} x + 4$

Step 1

Eliminate the equal sides of each equation and combine.

$x + 1 = - \frac{1}{2} x + 4$

Step 2

Solve $x + 1 = - \frac{1}{2} x + 4$ for $x$ .

Combine $x$ and $\frac{1}{2}$ .

$x + 1 = - \frac{x}{2} + 4$

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

Add $\frac{x}{2}$ to both sides of the equation.

$x + 1 + \frac{x}{2} = 4$

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

$x \cdot \frac{2}{2} + \frac{x}{2} + 1 = 4$

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

$\frac{x \cdot 2}{2} + \frac{x}{2} + 1 = 4$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{2} + 1 = 4$

Add $x \cdot 2$ and $x$ .

Reorder $x$ and $2$ .

$\frac{2 \cdot x + x}{2} + 1 = 4$

Add $2 \cdot x$ and $x$ .

$\frac{3 \cdot x}{2} + 1 = 4$

$\frac{3 x}{2} + 1 = 4$

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

Subtract $1$ from both sides of the equation.

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

Subtract $1$ from $4$ .

$\frac{3 x}{2} = 3$

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 3$

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{2}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x = \frac{2}{3} \cdot 3$

Rewrite the expression.

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

Substitute $2$ for $x$ .

$y = - \frac{1}{2} \cdot 2 + 4$

Substitute $2$ for $x$ in $y = - \frac{1}{2} \cdot 2 + 4$ and solve for $y$ .

Remove parentheses.

$y = - \frac{1}{2} \cdot 2 + 4$

Simplify $- \frac{1}{2} \cdot 2 + 4$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$y = \frac{- 1}{2} \cdot 2 + 4$

Cancel the common factor.

$y = \frac{- 1}{2} \cdot 2 + 4$

Rewrite the expression.

$y = - 1 + 4$

Add $- 1$ and $4$ .

$y = 3$

Step 4

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

$(2, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 6

Solve the System of Equations y=x+1 y=-1/2x+4

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