Download Solving Simple Simultaneous Equations

Solving Simple
Simultaneous Equations
Slideshow 12, Mr Richard Sasaki
Mathematics, Room 307
Objectives
• Review how to subtract polynomials in
vertical form
• Look at how simultaneous equations
work
• Solve simultaneous equations with one
coefficient and term the same.
Subtracting Polynomials Review
Subtracting Polynomials can be done
vertically, in the same way as subtracting two
numbers. We can calculate from left to right
or right to left.
Examples
19x + 8y
12𝑥 + 9𝑦
7𝑥 - 𝑦
Try the worksheet!
9𝑥 − 3𝑦
−3𝑥
+12𝑥5𝑦 − 8𝑦
Answers
𝑥 + 3𝑦
3𝑥 + 5𝑦
−5𝑥 − 3𝑦
−7𝑥 + 3𝑦
3𝑦
7𝑥 − 2𝑦
11𝑥 − 3𝑦
3½𝑥 + 5𝑦
3𝑥 − 9𝑦
−3𝑥 + 3𝑦
5𝑥 + 8𝑦
−4𝑥 + 5𝑦
Simultaneous Equations
Linear simultaneous equations with two unknowns
usually have two only one possibility for each
unknown. Each unknown only represents one number.
You may have realised this from last lesson.
Simultaneous means “at the same time”. These two
(or more) equations work together at the same time.
So how do we solve them?
Simultaneous Equations
Today, we will look at examples where a coefficient
and term are the same in each equation.
Example
Solve the simultaneous equations below.
What can we do to
①𝑥 + 5𝑦 = 8
solve for x or y?
②𝑥 + 3𝑦 = 6
Yes, let’s subtract the
2𝑦 = 2
①－
top from the bottom!
②
𝑦 = 1
Then we can remove
①
𝑥 + 5𝑦 = 8 x and solve for y.
Now we need to
substitute y = 1 into 𝑥 + 5(1) = 8
① or ②. Either are
𝑥 + 5 = 8 So 𝑥 = 3 and 𝑦 = 1.
okay!
Simultaneous Equations
Let’s try another example.
Example
Solve the simultaneous equations below.
Yes, let’s subtract the
①3𝑥 + 5𝑦 = 2
top from the bottom
②3𝑥 − 2𝑦 = 16
again. (Subtracting the
①－
②
7𝑦 = −14
𝑦 = −2
Substitute 𝑦 = __ ①3𝑥 + 5𝑦 = 2
into whichever 3𝑥 + 5(−2) = 2
looks easiest.
3𝑥 – 10 = 2
3𝑥 = 12
𝑥 = 4
bottom from the top is
also okay).
Once again, we can
remove 𝑥 and solve for
𝑦.
So 𝑥 = 4 and 𝑦 = −2.
Simultaneous Equations
So for a summary, to solve simultaneous equations like
this, we subtract one from another (doesn’t matter
which) and solve for the other unknown. Then we
substitute this into one of the equations (whichever
you like) and find the result for the other.
Remember to write your answer clearly at the end!
Good luck and try the worksheets!
Answers – Easy & Medium
2𝑦 = 4
It disappears.
2
0
3 8
5 2 -3 1
5𝑥 = 5
It disappears.
4𝑦 = 16
4
3
𝑎 = 4, 𝑏 = 1
2 3 -9 7
2 9
Answers – Hard
2
3 3
1
5 3
5 3
2 5
37
7
5 4
10
7