How do you solve the following system?: # 3x+3y= -7 , 3x − y = 30 #

Question

How do you solve the following system?: # 3x+3y= -7  ,   3x − y = 30   #

Eva Abramson · Accepted Answer

#y=-9 1/4, x=6 11/12#

#3x+3y=-7 -------1#

#3x-y=30--------2#

#4y=-37#----------------------------------#1-2#

#y=-37/4#

#y=-9 1/4#

substitute # y= -37/4# in-------2

#3x-(-37/4)=30#

#3x+37/4=30#

#3x=30-37/4#

#3x=120/4-37/4#

#3x=83/4#

multiply each side by four.

#12x=83#

#x=83/12#

#x=6 11/12#

substitute #y=-37/4, x= 83/12# in-------2

#3(83/12)-(-37/4)=30#

#249/12+37/4=30/1#

#(249+111=360)/12#

#249/12+111/12=360/12#

#360/12=360/12#

Avery Alexander · Answer

undefined To solve the system of equations:

1. Eliminate one variable by adding or subtracting the equations.
2. Solve for the remaining variable.
3. Substitute the value found into one of the original equations to solve for the other variable.
4. Check the solution by substituting the values back into both equations.

Given the system:
$$3x + 3y = -7$$
$$3x - y = 30$$

Step 1: Eliminate one variable
$$3x + 3y = -7$$
$$3x - y = 30$$

Adding the equations eliminates $3x$:
$$3x + 3y + 3x - y = -7 + 30$$
$$6x + 2y = 23$$

Step 2: Solve for the remaining variable
$$6x + 2y = 23$$
$$y = \frac{23 - 6x}{2}$$

Step 3: Substitute the value found into one of the original equations
$$3x - y = 30$$
$$3x - \frac{23 - 6x}{2} = 30$$

Step 4: Solve for $x$
$$6x - 23 + 12x = 60$$
$$18x = 83$$
$$x = \frac{83}{18}$$

Step 5: Substitute the value of $x$ back into one of the original equations to find $y$
$$3x + 3y = -7$$
$$3 \left(\frac{83}{18}\right) + 3y = -7$$
$$y = -\frac{77}{18}$$

The solution to the system is $x = \frac{83}{18}$ and $y = -\frac{77}{18}$.