Solve the System of Equations y=5x+2 3x=-y+10

$y = 5 x + 2$ $3 x = - y + 10$

Step 1

Replace all occurrences of $y$ with $5 x + 2$ in each equation.

Replace all occurrences of $y$ in $3 x = - y + 10$ with $5 x + 2$ .

$3 x = - (5 x + 2) + 10$

$y = 5 x + 2$

Simplify the right side.

Simplify $- (5 x + 2) + 10$ .

Simplify each term.

Apply the distributive property.

$3 x = - (5 x) - 1 \cdot 2 + 10$

$y = 5 x + 2$

Multiply $5$ by $- 1$ .

$3 x = - 5 x - 1 \cdot 2 + 10$

$y = 5 x + 2$

Multiply $- 1$ by $2$ .

$3 x = - 5 x - 2 + 10$

$y = 5 x + 2$

$3 x = - 5 x - 2 + 10$

$y = 5 x + 2$

Add $- 2$ and $10$ .

$3 x = - 5 x + 8$

$y = 5 x + 2$

$3 x = - 5 x + 8$

$y = 5 x + 2$

$3 x = - 5 x + 8$

$y = 5 x + 2$

$3 x = - 5 x + 8$

$y = 5 x + 2$

Step 2

Solve for $x$ in $3 x = - 5 x + 8$ .

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

Add $5 x$ to both sides of the equation.

$3 x + 5 x = 8$

$y = 5 x + 2$

Add $3 x$ and $5 x$ .

$8 x = 8$

$y = 5 x + 2$

$8 x = 8$

$y = 5 x + 2$

Divide each term in $8 x = 8$ by $8$ and simplify.

Divide each term in $8 x = 8$ by $8$ .

$\frac{8 x}{8} = \frac{8}{8}$

$y = 5 x + 2$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{8}{8}$

$y = 5 x + 2$

Divide $x$ by $1$ .

$x = \frac{8}{8}$

$y = 5 x + 2$

$x = \frac{8}{8}$

$y = 5 x + 2$

$x = \frac{8}{8}$

$y = 5 x + 2$

Simplify the right side.

Divide $8$ by $8$ .

$x = 1$

$y = 5 x + 2$

$x = 1$

$y = 5 x + 2$

$x = 1$

$y = 5 x + 2$

$x = 1$

$y = 5 x + 2$

Step 3

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = 5 x + 2$ with $1$ .

$y = 5 (1) + 2$

$x = 1$

Simplify the right side.

Simplify $5 (1) + 2$ .

Multiply $5$ by $1$ .

$y = 5 + 2$

$x = 1$

Add $5$ and $2$ .

$y = 7$

$x = 1$

$y = 7$

$x = 1$

$y = 7$

$x = 1$

$y = 7$

$x = 1$

Step 4

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

$(1, 7)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 7)$

Equation Form:

$x = 1, y = 7$

Step 6

Solve the System of Equations y=5x+2 3x=-y+10

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