Solve by Substitution y=3x+8 , 5x+2y=5

$y = 3 x + 8$ , $5 x + 2 y = 5$

Step 1

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

Replace all occurrences of $y$ in $5 x + 2 y = 5$ with $3 x + 8$ .

$5 x + 2 (3 x + 8) = 5$

$y = 3 x + 8$

Simplify the left side.

Simplify $5 x + 2 (3 x + 8)$ .

Simplify each term.

Apply the distributive property.

$5 x + 2 (3 x) + 2 \cdot 8 = 5$

$y = 3 x + 8$

Multiply $3$ by $2$ .

$5 x + 6 x + 2 \cdot 8 = 5$

$y = 3 x + 8$

Multiply $2$ by $8$ .

$5 x + 6 x + 16 = 5$

$y = 3 x + 8$

$5 x + 6 x + 16 = 5$

$y = 3 x + 8$

Add $5 x$ and $6 x$ .

$11 x + 16 = 5$

$y = 3 x + 8$

$11 x + 16 = 5$

$y = 3 x + 8$

$11 x + 16 = 5$

$y = 3 x + 8$

$11 x + 16 = 5$

$y = 3 x + 8$

Step 2

Solve for $x$ in $11 x + 16 = 5$ .

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

Subtract $16$ from both sides of the equation.

$11 x = 5 - 16$

$y = 3 x + 8$

Subtract $16$ from $5$ .

$11 x = - 11$

$y = 3 x + 8$

$11 x = - 11$

$y = 3 x + 8$

Divide each term in $11 x = - 11$ by $11$ and simplify.

Divide each term in $11 x = - 11$ by $11$ .

$\frac{11 x}{11} = \frac{- 11}{11}$

$y = 3 x + 8$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{- 11}{11}$

$y = 3 x + 8$

Divide $x$ by $1$ .

$x = \frac{- 11}{11}$

$y = 3 x + 8$

$x = \frac{- 11}{11}$

$y = 3 x + 8$

$x = \frac{- 11}{11}$

$y = 3 x + 8$

Simplify the right side.

Divide $- 11$ by $11$ .

$x = - 1$

$y = 3 x + 8$

$x = - 1$

$y = 3 x + 8$

$x = - 1$

$y = 3 x + 8$

$x = - 1$

$y = 3 x + 8$

Step 3

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

Replace all occurrences of $x$ in $y = 3 x + 8$ with $- 1$ .

$y = 3 (- 1) + 8$

$x = - 1$

Simplify the right side.

Simplify $3 (- 1) + 8$ .

Multiply $3$ by $- 1$ .

$y = - 3 + 8$

$x = - 1$

Add $- 3$ and $8$ .

$y = 5$

$x = - 1$

$y = 5$

$x = - 1$

$y = 5$

$x = - 1$

$y = 5$

$x = - 1$

Step 4

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

$(- 1, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, 5)$

Equation Form:

$x = - 1, y = 5$

Step 6

Solve by Substitution y=3x+8 , 5x+2y=5

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