Section 4.3 Systems of Equations and
Elimination
So we’ve learned how to solve systems of equations using graphs and substitution. Now
we learn to solve using addition (I think, my favorite).
This is where Ax + By = C comes in handy.
We’re going to work a bunch of problems, but, first, something you need to remember.
 if a = b and
c = d then
a+c=b+d
Example:
Watch what happens when we add these equations together.
5x – y = 14
-5x +2y = -13
With addition, we are eliminating the x term.
5x – y = 14
-5x +2y = -13
0 +y=1
y=1
Now, plug 1 in for y in either equation
and solve for x.
5x – (1) = 14
5x = 15
x=3
The answer is……(3, 1).
It’s always a good idea to check the answer in each equation.
Example:
Now, with a little twist.
5x – 4y = 19 If you look at the equations carefully, you can see that 3x + 2y = 7
multiply the second one by 2, then add the
equations, the y term will drop out (add up to zero).
5x – 4y = 19
6x + 4y = 14
11x + 0 = 33
11x = 33
x = 3 Now, plug this in one of the equations and solve for y.
3(3) + 2y = 7
9 + 2y = 7
2y = -2
y = -1 The answer is…..(3, -1)
Of course, you would check this in each equation to make SURE it’s correct.
Example:
2x + 3y = -16
5x – 10y = 30
A little different.
We’re going to have to work on both equations in
order to get a term to drop out. Since the y’s are
already opposite in sign, let’s multiply the first
equation by 10 and the second equation by 3.
10(2x + 3y = -16)
3(5x – 10y = 30)
20x + 30y = -160
15x – 30y = 90
35 x + 0 = -70
35x = -70
x = -2
2(-2) + 3y = -16
-4 + 3y = -16
3y = -12
y = -4
Now, add.
Now, plug -2 in for x in one of the equations.
The answer is………(-2, -4)
if you
Practice:
7x – 3y = 4
-14x + 6y = -7
x + 3y = 2
3x + 9y = 6
3 things to note:
1) You will most likely get one solution, an ordered pair.
2) If the variables drop out and you get a false statement, there is no solution.
3) If the variables drop out and you get a true statement, there are infinitely many
solutions (it’s basically the same line).
Homework: MLP (MyLabsPlus) and the following problems from the text.
1-4
Just answer the question.
39, 48
Work the problems as demonstrated in class.
MLP problems & Quiz are due ________
Text problems are due _________