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

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

Step 1

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

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

$5 x + 3 x = 8$

$y = 3 x$

Simplify the left side.

Simplify $5 x + 3 x$ .

Remove parentheses.

$5 x + 3 x = 8$

$y = 3 x$

Add $5 x$ and $3 x$ .

$8 x = 8$

$y = 3 x$

$8 x = 8$

$y = 3 x$

$8 x = 8$

$y = 3 x$

$8 x = 8$

$y = 3 x$

Step 2

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

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

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

$y = 3 x$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

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

$y = 3 x$

Divide $x$ by $1$ .

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

$y = 3 x$

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

$y = 3 x$

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

$y = 3 x$

Simplify the right side.

Divide $8$ by $8$ .

$x = 1$

$y = 3 x$

$x = 1$

$y = 3 x$

$x = 1$

$y = 3 x$

Step 3

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

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

$y = 3 (1)$

$x = 1$

Simplify the right side.

Multiply $3$ by $1$ .

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

Step 4

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

$(1, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 6

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

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