Solve the System of Equations 3x+y=12 and -x-4y=29

$3 x + y = 12$ and $- x - 4 y = 29$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = 12 - 3 x$

$- x - 4 y = 29$

Step 2

Replace all occurrences of $y$ with $12 - 3 x$ in each equation.

Replace all occurrences of $y$ in $- x - 4 y = 29$ with $12 - 3 x$ .

$- x - 4 (12 - 3 x) = 29$

$y = 12 - 3 x$

Simplify the left side.

Simplify $- x - 4 (12 - 3 x)$ .

Simplify each term.

Apply the distributive property.

$- x - 4 \cdot 12 - 4 (- 3 x) = 29$

$y = 12 - 3 x$

Multiply $- 4$ by $12$ .

$- x - 48 - 4 (- 3 x) = 29$

$y = 12 - 3 x$

Multiply $- 3$ by $- 4$ .

$- x - 48 + 12 x = 29$

$y = 12 - 3 x$

$- x - 48 + 12 x = 29$

$y = 12 - 3 x$

Add $- x$ and $12 x$ .

$11 x - 48 = 29$

$y = 12 - 3 x$

$11 x - 48 = 29$

$y = 12 - 3 x$

$11 x - 48 = 29$

$y = 12 - 3 x$

$11 x - 48 = 29$

$y = 12 - 3 x$

Step 3

Solve for $x$ in $11 x - 48 = 29$ .

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

Add $48$ to both sides of the equation.

$11 x = 29 + 48$

$y = 12 - 3 x$

Add $29$ and $48$ .

$11 x = 77$

$y = 12 - 3 x$

$11 x = 77$

$y = 12 - 3 x$

Divide each term in $11 x = 77$ by $11$ and simplify.

Divide each term in $11 x = 77$ by $11$ .

$\frac{11 x}{11} = \frac{77}{11}$

$y = 12 - 3 x$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{77}{11}$

$y = 12 - 3 x$

Divide $x$ by $1$ .

$x = \frac{77}{11}$

$y = 12 - 3 x$

$x = \frac{77}{11}$

$y = 12 - 3 x$

$x = \frac{77}{11}$

$y = 12 - 3 x$

Simplify the right side.

Divide $77$ by $11$ .

$x = 7$

$y = 12 - 3 x$

$x = 7$

$y = 12 - 3 x$

$x = 7$

$y = 12 - 3 x$

$x = 7$

$y = 12 - 3 x$

Step 4

Replace all occurrences of $x$ with $7$ in each equation.

Replace all occurrences of $x$ in $y = 12 - 3 x$ with $7$ .

$y = 12 - 3 \cdot 7$

$x = 7$

Simplify the right side.

Simplify $12 - 3 \cdot 7$ .

Multiply $- 3$ by $7$ .

$y = 12 - 21$

$x = 7$

Subtract $21$ from $12$ .

$y = - 9$

$x = 7$

$y = - 9$

$x = 7$

$y = - 9$

$x = 7$

$y = - 9$

$x = 7$

Step 5

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

$(7, - 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, - 9)$

Equation Form:

$x = 7, y = - 9$

Step 7

Solve the System of Equations 3x+y=12 and -x-4y=29

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