Solve the System of Equations 4x+y=1 -20x-6y=5

$4 x + y = 1$ $- 20 x - 6 y = 5$

Step 1

Subtract $4 x$ from both sides of the equation.

$y = 1 - 4 x$

$- 20 x - 6 y = 5$

Step 2

Replace all occurrences of $y$ with $1 - 4 x$ in each equation.

Replace all occurrences of $y$ in $- 20 x - 6 y = 5$ with $1 - 4 x$ .

$- 20 x - 6 (1 - 4 x) = 5$

$y = 1 - 4 x$

Simplify the left side.

Simplify $- 20 x - 6 (1 - 4 x)$ .

Simplify each term.

Apply the distributive property.

$- 20 x - 6 \cdot 1 - 6 (- 4 x) = 5$

$y = 1 - 4 x$

Multiply $- 6$ by $1$ .

$- 20 x - 6 - 6 (- 4 x) = 5$

$y = 1 - 4 x$

Multiply $- 4$ by $- 6$ .

$- 20 x - 6 + 24 x = 5$

$y = 1 - 4 x$

$- 20 x - 6 + 24 x = 5$

$y = 1 - 4 x$

Add $- 20 x$ and $24 x$ .

$4 x - 6 = 5$

$y = 1 - 4 x$

$4 x - 6 = 5$

$y = 1 - 4 x$

$4 x - 6 = 5$

$y = 1 - 4 x$

$4 x - 6 = 5$

$y = 1 - 4 x$

Step 3

Solve for $x$ in $4 x - 6 = 5$ .

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

Add $6$ to both sides of the equation.

$4 x = 5 + 6$

$y = 1 - 4 x$

Add $5$ and $6$ .

$4 x = 11$

$y = 1 - 4 x$

$4 x = 11$

$y = 1 - 4 x$

Divide each term in $4 x = 11$ by $4$ and simplify.

Divide each term in $4 x = 11$ by $4$ .

$\frac{4 x}{4} = \frac{11}{4}$

$y = 1 - 4 x$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{11}{4}$

$y = 1 - 4 x$

Divide $x$ by $1$ .

$x = \frac{11}{4}$

$y = 1 - 4 x$

$x = \frac{11}{4}$

$y = 1 - 4 x$

$x = \frac{11}{4}$

$y = 1 - 4 x$

$x = \frac{11}{4}$

$y = 1 - 4 x$

$x = \frac{11}{4}$

$y = 1 - 4 x$

Step 4

Replace all occurrences of $x$ with $\frac{11}{4}$ in each equation.

Replace all occurrences of $x$ in $y = 1 - 4 x$ with $\frac{11}{4}$ .

$y = 1 - 4 (\frac{11}{4})$

$x = \frac{11}{4}$

Simplify the right side.

Simplify $1 - 4 (\frac{11}{4})$ .

Simplify each term.

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$y = 1 + 4 (- 1) (\frac{11}{4})$

$x = \frac{11}{4}$

Cancel the common factor.

$y = 1 + 4 \cdot (- 1 (\frac{11}{4}))$

$x = \frac{11}{4}$

Rewrite the expression.

$y = 1 - 1 \cdot 11$

$x = \frac{11}{4}$

$y = 1 - 1 \cdot 11$

$x = \frac{11}{4}$

Multiply $- 1$ by $11$ .

$y = 1 - 11$

$x = \frac{11}{4}$

$y = 1 - 11$

$x = \frac{11}{4}$

Subtract $11$ from $1$ .

$y = - 10$

$x = \frac{11}{4}$

$y = - 10$

$x = \frac{11}{4}$

$y = - 10$

$x = \frac{11}{4}$

$y = - 10$

$x = \frac{11}{4}$

Step 5

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

$(\frac{11}{4}, - 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{11}{4}, - 10)$

Equation Form:

$x = \frac{11}{4}, y = - 10$

Step 7

Solve the System of Equations 4x+y=1 -20x-6y=5

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