Solve by Substitution 4x-5y=-7 , y=5x

$4 x - 5 y = - 7$ , $y = 5 x$

Step 1

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

Replace all occurrences of $y$ in $4 x - 5 y = - 7$ with $5 x$ .

$4 x - 5 (5 x) = - 7$

$y = 5 x$

Simplify the left side.

Simplify $4 x - 5 (5 x)$ .

Multiply $5$ by $- 5$ .

$4 x - 25 x = - 7$

$y = 5 x$

Subtract $25 x$ from $4 x$ .

$- 21 x = - 7$

$y = 5 x$

$- 21 x = - 7$

$y = 5 x$

$- 21 x = - 7$

$y = 5 x$

$- 21 x = - 7$

$y = 5 x$

Step 2

Divide each term in $- 21 x = - 7$ by $- 21$ and simplify.

Divide each term in $- 21 x = - 7$ by $- 21$ .

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

$y = 5 x$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

$y = 5 x$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 21}$

$y = 5 x$

$x = \frac{- 7}{- 21}$

$y = 5 x$

$x = \frac{- 7}{- 21}$

$y = 5 x$

Simplify the right side.

Cancel the common factor of $- 7$ and $- 21$ .

Factor $- 7$ out of $- 7$ .

$x = \frac{- 7 \cdot 1}{- 21}$

$y = 5 x$

Cancel the common factors.

Factor $- 7$ out of $- 21$ .

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

$y = 5 x$

Cancel the common factor.

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

$y = 5 x$

Rewrite the expression.

$x = \frac{1}{3}$

$y = 5 x$

$x = \frac{1}{3}$

$y = 5 x$

$x = \frac{1}{3}$

$y = 5 x$

$x = \frac{1}{3}$

$y = 5 x$

$x = \frac{1}{3}$

$y = 5 x$

Step 3

Replace all occurrences of $x$ with $\frac{1}{3}$ in each equation.

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

$y = 5 (\frac{1}{3})$

$x = \frac{1}{3}$

Simplify the right side.

Combine $5$ and $\frac{1}{3}$ .

$y = \frac{5}{3}$

$x = \frac{1}{3}$

$y = \frac{5}{3}$

$x = \frac{1}{3}$

$y = \frac{5}{3}$

$x = \frac{1}{3}$

Step 4

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

$(\frac{1}{3}, \frac{5}{3})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{1}{3}, \frac{5}{3})$

Equation Form:

$x = \frac{1}{3}, y = \frac{5}{3}$

Step 6

Solve by Substitution 4x-5y=-7 , y=5x

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