Solve the System of Equations 4x+2y=7 y=5x

$4 x + 2 y = 7$ $y = 5 x$

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

Replace all occurrences of $y$ in $4 x + 2 y = 7$ with $5 x$ .

$4 x + 2 (5 x) = 7$

$y = 5 x$

Simplify the left side.

Simplify $4 x + 2 (5 x)$ .

Multiply $5$ by $2$ .

$4 x + 10 x = 7$

$y = 5 x$

Add $4 x$ and $10 x$ .

$14 x = 7$

$y = 5 x$

$14 x = 7$

$y = 5 x$

$14 x = 7$

$y = 5 x$

$14 x = 7$

$y = 5 x$

Divide each term in $14 x = 7$ by $14$ and simplify.

Divide each term in $14 x = 7$ by $14$ .

$\frac{14 x}{14} = \frac{7}{14}$

$y = 5 x$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} = \frac{7}{14}$

$y = 5 x$

Divide $x$ by $1$ .

$x = \frac{7}{14}$

$y = 5 x$

$x = \frac{7}{14}$

$y = 5 x$

$x = \frac{7}{14}$

$y = 5 x$

Simplify the right side.

Cancel the common factor of $7$ and $14$ .

Factor $7$ out of $7$ .

$x = \frac{7 (1)}{14}$

$y = 5 x$

Cancel the common factors.

Factor $7$ out of $14$ .

$x = \frac{7 \cdot 1}{7 \cdot 2}$

$y = 5 x$

Cancel the common factor.

$x = \frac{7 \cdot 1}{7 \cdot 2}$

$y = 5 x$

Rewrite the expression.

$x = \frac{1}{2}$

$y = 5 x$

$x = \frac{1}{2}$

$y = 5 x$

$x = \frac{1}{2}$

$y = 5 x$

$x = \frac{1}{2}$

$y = 5 x$

$x = \frac{1}{2}$

$y = 5 x$

Replace all occurrences of $x$ with $\frac{1}{2}$ in each equation.

Replace all occurrences of $x$ in $y = 5 x$ with $\frac{1}{2}$ .

$y = 5 (\frac{1}{2})$

$x = \frac{1}{2}$

Simplify the right side.

Combine $5$ and $\frac{1}{2}$ .

$y = \frac{5}{2}$

$x = \frac{1}{2}$

$y = \frac{5}{2}$

$x = \frac{1}{2}$

$y = \frac{5}{2}$

$x = \frac{1}{2}$

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

$(\frac{1}{2}, \frac{5}{2})$

The result can be shown in multiple forms.

Point Form:

$(\frac{1}{2}, \frac{5}{2})$

Equation Form:

$x = \frac{1}{2}, y = \frac{5}{2}$

Solve the System of Equations 4x+2y=7 y=5x

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