Solve the System of Equations 3x+2y=6 y=-5/2x+1

$3 x + 2 y = 6$ $y = - \frac{5}{2} x + 1$

Simplify each term.

Combine $x$ and $\frac{5}{2}$ .

$y = - \frac{x \cdot 5}{2} + 1$

$3 x + 2 y = 6$

Move $5$ to the left of $x$ .

$y = - \frac{5 x}{2} + 1$

$3 x + 2 y = 6$

$y = - \frac{5 x}{2} + 1$

$3 x + 2 y = 6$

Replace all occurrences of $y$ with $- \frac{5 x}{2} + 1$ in each equation.

Replace all occurrences of $y$ in $3 x + 2 y = 6$ with $- \frac{5 x}{2} + 1$ .

$3 x + 2 (- \frac{5 x}{2} + 1) = 6$

$y = - \frac{5 x}{2} + 1$

Simplify the left side.

Simplify $3 x + 2 (- \frac{5 x}{2} + 1)$ .

Simplify each term.

Apply the distributive property.

$3 x + 2 (- \frac{5 x}{2}) + 2 \cdot 1 = 6$

$y = - \frac{5 x}{2} + 1$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$3 x + 2 (\frac{- 5 x}{2}) + 2 \cdot 1 = 6$

$y = - \frac{5 x}{2} + 1$

Cancel the common factor.

$3 x + 2 (\frac{- 5 x}{2}) + 2 \cdot 1 = 6$

$y = - \frac{5 x}{2} + 1$

Rewrite the expression.

$3 x - 5 x + 2 \cdot 1 = 6$

$y = - \frac{5 x}{2} + 1$

$3 x - 5 x + 2 \cdot 1 = 6$

$y = - \frac{5 x}{2} + 1$

Multiply $2$ by $1$ .

$3 x - 5 x + 2 = 6$

$y = - \frac{5 x}{2} + 1$

$3 x - 5 x + 2 = 6$

$y = - \frac{5 x}{2} + 1$

Subtract $5 x$ from $3 x$ .

$- 2 x + 2 = 6$

$y = - \frac{5 x}{2} + 1$

$- 2 x + 2 = 6$

$y = - \frac{5 x}{2} + 1$

$- 2 x + 2 = 6$

$y = - \frac{5 x}{2} + 1$

$- 2 x + 2 = 6$

$y = - \frac{5 x}{2} + 1$

Solve for $x$ in $- 2 x + 2 = 6$ .

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

Subtract $2$ from both sides of the equation.

$- 2 x = 6 - 2$

$y = - \frac{5 x}{2} + 1$

Subtract $2$ from $6$ .

$- 2 x = 4$

$y = - \frac{5 x}{2} + 1$

$- 2 x = 4$

$y = - \frac{5 x}{2} + 1$

Divide each term in $- 2 x = 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = 4$ by $- 2$ .

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

$y = - \frac{5 x}{2} + 1$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$y = - \frac{5 x}{2} + 1$

Divide $x$ by $1$ .

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

$y = - \frac{5 x}{2} + 1$

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

$y = - \frac{5 x}{2} + 1$

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

$y = - \frac{5 x}{2} + 1$

Simplify the right side.

Divide $4$ by $- 2$ .

$x = - 2$

$y = - \frac{5 x}{2} + 1$

$x = - 2$

$y = - \frac{5 x}{2} + 1$

$x = - 2$

$y = - \frac{5 x}{2} + 1$

$x = - 2$

$y = - \frac{5 x}{2} + 1$

Replace all occurrences of $x$ with $- 2$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{5 x}{2} + 1$ with $- 2$ .

$y = - \frac{5 (- 2)}{2} + 1$

$x = - 2$

Simplify the right side.

Simplify $- \frac{5 (- 2)}{2} + 1$ .

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $5 (- 2)$ .

$y = - \frac{2 (5 \cdot (- 1))}{2} + 1$

$x = - 2$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = - \frac{2 (5 \cdot (- 1))}{2 (1)} + 1$

$x = - 2$

Cancel the common factor.

$y = - \frac{2 (5 \cdot (- 1))}{2 \cdot 1} + 1$

$x = - 2$

Rewrite the expression.

$y = - \frac{5 \cdot (- 1)}{1} + 1$

$x = - 2$

Divide $5 \cdot (- 1)$ by $1$ .

$y = - (5 \cdot (- 1)) + 1$

$x = - 2$

$y = - (5 \cdot (- 1)) + 1$

$x = - 2$

$y = - (5 \cdot (- 1)) + 1$

$x = - 2$

Multiply $5$ by $- 1$ .

$y = 5 + 1$

$x = - 2$

Multiply $- 1$ by $- 5$ .

$y = 5 + 1$

$x = - 2$

$y = 5 + 1$

$x = - 2$

Add $5$ and $1$ .

$y = 6$

$x = - 2$

$y = 6$

$x = - 2$

$y = 6$

$x = - 2$

$y = 6$

$x = - 2$

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

$(- 2, 6)$

The result can be shown in multiple forms.

Point Form:

$(- 2, 6)$

Equation Form:

$x = - 2, y = 6$

Solve the System of Equations 3x+2y=6 y=-5/2x+1

Related Questions

Support LCMGCF.com by disabling your adblocker.