Answer:
Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down
to one with only one variable (by substitution or addition). With three variables
we will reduce the system down to one with two variables (usually by addition),
which we can then solve by either addition or substitution.
To reduce from three variables down to two it is very important to keep the work
organized. We will use addition with two equations to eliminate one variable.
This new equation we will call (A). Then we will use a different pair of equations
and use addition to eliminate the same variable. This second new equation we
will call (B). Once we have done this we will have two equations (A) and (B)
with the same two variables that we can solve using either method. This is shown
in the following examples.
Example 1.
3x +2y − z = − 1
− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations
5x +2y − z = 3
Step-by-step explanation:
Answer:
x = 7
Step-by-step explanation:
The sum of interior angles is equal to 360°
9x - 4 + 8x + 2 + 13x + 30 + 19x - 11 = 360° add like terms
49x + 17 = 360 subtract 17 from both sides
49x = 343 divide both sides by 49
x = 7
replace x with the value we found to calculate each angle.
Answer:
Step-by-step explanation:
total time is 5 hr and total distance is 72 nautical miles
Answer:
30 oz of dog food
Step-by-step explanation:
you want to multiply the number 6 over the number of dogs there are and there are 5 so that is 5•6 which =30
Answer:
The company sold 100 widgets and 250 gizmos.
Step-by-step explanation:
Let 
be the number of widgets sold and 
be the number of gizmos sold.
We are told that the company sold 350 items. We can represent this information in an equation as:
We have been given that a each widget sold for $35 and each gizmo sold for $22. The company sold 350 items for a total of $9,000.
We can represent this information in an equation as:
From equation (1), we will get:
Substitute this value in equation (2):
Therefore, the company sold 100 widgets.
Substitute in equation (1):
Therefore, the company sold 250 gizmos.
