Solve the System of Equations y=3/2x+2 y=1/2x+4

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

Eliminate the equal sides of each equation and combine.

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

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

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

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

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

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

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

Subtract $\frac{x}{2}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $x$ from $3 x$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$2 + x = 4$

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

Subtract $2$ from both sides of the equation.

$x = 4 - 2$

Subtract $2$ from $4$ .

$x = 2$

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 $y$ .

Multiply $\frac{1}{2}$ by $2$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 1 + 4$

Add $1$ and $4$ .

$y = 5$

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

$(2, 5)$

The result can be shown in multiple forms.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

Solve the System of Equations y=3/2x+2 y=1/2x+4

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