Solve the System of Equations y=3x-6 y=-1/2x+8

$y = 3 x - 6$ $y = - \frac{1}{2} x + 8$

Step 1

Eliminate the equal sides of each equation and combine.

$3 x - 6 = - \frac{1}{2} x + 8$

Step 2

Solve $3 x - 6 = - \frac{1}{2} x + 8$ for $x$ .

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

$3 x - 6 = - \frac{x}{2} + 8$

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

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

$3 x - 6 + \frac{x}{2} = 8$

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 x \cdot \frac{2}{2} + \frac{x}{2} - 6 = 8$

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

$\frac{3 x \cdot 2}{2} + \frac{x}{2} - 6 = 8$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 + x}{2} - 6 = 8$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x \cdot 2 + x$ .

Factor $x$ out of $3 x \cdot 2$ .

$\frac{x (3 \cdot 2) + x}{2} - 6 = 8$

Raise $x$ to the power of $1$ .

$\frac{x (3 \cdot 2) + x^{1}}{2} - 6 = 8$

Factor $x$ out of $x^{1}$ .

$\frac{x (3 \cdot 2) + x \cdot 1}{2} - 6 = 8$

Factor $x$ out of $x (3 \cdot 2) + x \cdot 1$ .

$\frac{x (3 \cdot 2 + 1)}{2} - 6 = 8$

Multiply $3$ by $2$ .

$\frac{x (6 + 1)}{2} - 6 = 8$

Add $6$ and $1$ .

$\frac{x \cdot 7}{2} - 6 = 8$

Move $7$ to the left of $x$ .

$\frac{7 x}{2} - 6 = 8$

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

Add $6$ to both sides of the equation.

$\frac{7 x}{2} = 8 + 6$

Add $8$ and $6$ .

$\frac{7 x}{2} = 14$

Multiply both sides of the equation by $\frac{2}{7}$ .

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 14$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{7} \cdot \frac{7 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 14$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 14$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{2}{7} \cdot 14$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 14$

Rewrite the expression.

$x = \frac{2}{7} \cdot 14$

Simplify the right side.

Simplify $\frac{2}{7} \cdot 14$ .

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$x = \frac{2}{7} \cdot (7 (2))$

Cancel the common factor.

$x = \frac{2}{7} \cdot (7 \cdot 2)$

Rewrite the expression.

$x = 2 \cdot 2$

Multiply $2$ by $2$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

Substitute $4$ for $x$ .

$y = - \frac{1}{2} \cdot 4 + 8$

Substitute $4$ for $x$ in $y = - \frac{1}{2} \cdot 4 + 8$ and solve for $y$ .

Remove parentheses.

$y = - \frac{1}{2} \cdot 4 + 8$

Simplify $- \frac{1}{2} \cdot 4 + 8$ .

Simplify each term.

Cancel the common factor of $2$ .

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

$y = \frac{- 1}{2} \cdot 4 + 8$

Factor $2$ out of $4$ .

$y = \frac{- 1}{2} \cdot (2 (2)) + 8$

Cancel the common factor.

$y = \frac{- 1}{2} \cdot (2 \cdot 2) + 8$

Rewrite the expression.

$y = - 1 \cdot 2 + 8$

Multiply $- 1$ by $2$ .

$y = - 2 + 8$

Add $- 2$ and $8$ .

$y = 6$

Step 4

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

$(4, 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 6)$

Equation Form:

$x = 4, y = 6$

Step 6

Solve the System of Equations y=3x-6 y=-1/2x+8

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