Solve the System of Equations 7x-2y=-6 8x+y=3

$7 x - 2 y = - 6$ $8 x + y = 3$

Step 1

Subtract $8 x$ from both sides of the equation.

$y = 3 - 8 x$

$7 x - 2 y = - 6$

Step 2

Replace all occurrences of $y$ with $3 - 8 x$ in each equation.

Replace all occurrences of $y$ in $7 x - 2 y = - 6$ with $3 - 8 x$ .

$7 x - 2 (3 - 8 x) = - 6$

$y = 3 - 8 x$

Simplify the left side.

Simplify $7 x - 2 (3 - 8 x)$ .

Simplify each term.

Apply the distributive property.

$7 x - 2 \cdot 3 - 2 (- 8 x) = - 6$

$y = 3 - 8 x$

Multiply $- 2$ by $3$ .

$7 x - 6 - 2 (- 8 x) = - 6$

$y = 3 - 8 x$

Multiply $- 8$ by $- 2$ .

$7 x - 6 + 16 x = - 6$

$y = 3 - 8 x$

$7 x - 6 + 16 x = - 6$

$y = 3 - 8 x$

Add $7 x$ and $16 x$ .

$23 x - 6 = - 6$

$y = 3 - 8 x$

$23 x - 6 = - 6$

$y = 3 - 8 x$

$23 x - 6 = - 6$

$y = 3 - 8 x$

$23 x - 6 = - 6$

$y = 3 - 8 x$

Step 3

Solve for $x$ in $23 x - 6 = - 6$ .

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

Add $6$ to both sides of the equation.

$23 x = - 6 + 6$

$y = 3 - 8 x$

Add $- 6$ and $6$ .

$23 x = 0$

$y = 3 - 8 x$

$23 x = 0$

$y = 3 - 8 x$

Divide each term in $23 x = 0$ by $23$ and simplify.

Divide each term in $23 x = 0$ by $23$ .

$\frac{23 x}{23} = \frac{0}{23}$

$y = 3 - 8 x$

Simplify the left side.

Cancel the common factor of $23$ .

Cancel the common factor.

$\frac{23 x}{23} = \frac{0}{23}$

$y = 3 - 8 x$

Divide $x$ by $1$ .

$x = \frac{0}{23}$

$y = 3 - 8 x$

$x = \frac{0}{23}$

$y = 3 - 8 x$

$x = \frac{0}{23}$

$y = 3 - 8 x$

Simplify the right side.

Divide $0$ by $23$ .

$x = 0$

$y = 3 - 8 x$

$x = 0$

$y = 3 - 8 x$

$x = 0$

$y = 3 - 8 x$

$x = 0$

$y = 3 - 8 x$

Step 4

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $y = 3 - 8 x$ with $0$ .

$y = 3 - 8 \cdot 0$

$x = 0$

Simplify the right side.

Simplify $3 - 8 \cdot 0$ .

Multiply $- 8$ by $0$ .

$y = 3 + 0$

$x = 0$

Add $3$ and $0$ .

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

Step 5

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

$(0, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, 3)$

Equation Form:

$x = 0, y = 3$

Step 7

Solve the System of Equations 7x-2y=-6 8x+y=3

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