1. Relationships between unknowns and Simultaneous Equations SLIDESHOW 11, MR RICHARD SASAKI ROOM 307, MATHEMATICS

2. OBJECTIVES Looking at how unknowns balance in an equation Checking whether unknowns can substitute into simultaneous equations properly

3. EQUATIONS When we have a single equation with an unknown, we can solve it. But when there are two or more we cannot. Both affect the equation.

4. EXAMPLE A non-alcoholic cocktail is made with mango and passion fruit. Let’s look at how the measures can relate as a percentage. Mango Passion fruit 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%10%20%30% 40% 50%60%70%80%90% Here, we can see that for the drink… Mango + Passion fruit = 100%

5. We can’t calculate much with two unknowns unless we know one of them. But there are specific values for two unknowns for a pair of equations. We call this pair of equations “Simultaneous Equations”. SIMULTANEOUS EQUATIONS

6. This lesson we are interested in testing the equations to see if the given unknowns work. SIMULTANEOUS EQUATIONS Example Look at the simultaneous equations below. Without solving, show that x = 5 and y = 2. To do this, we substitute x = 5, y = 2 into the equations and check to see if there is a balance.

7. That example worked. Let’s try another. SIMULTANEOUS EQUATIONS Example Look at the simultaneous equations below. As you can see, this pair didn’t work. Try the worksheets!

8. ANSWERS 0 12345 6 78 9 10 11 12 13 14 15 smaller bigger smaller bigger 4 and 5 20 1 and 8 8 9 8 72 3 and 6, 6 and 3, 4 and 5, 5 and 4 4 3(4) + 2(1) = 14 5(6) + 3(5) = 45 5(7) + 3(4) = 47 9(7) - 2(4) = 55 4x + 3y = -1 (÷13) Because the two numbers added make a negative. Because a number squared is always positive. 4(2) + 3(-3) = -1 4 + 9 = 13