Relationships between unknowns and Simultaneous Equations

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. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 10% 20% 30% 50% 60% 70% 80% 90% 40% Here, we can see that for the drink… Mango + Passion fruit = 100%

5. Simultaneous equations • 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”. For and , what are and ? Yes, is and is . You may have already started this in Japanese maths. We’ll look at this next lesson.

6. Simultaneous equations • This lesson we are interested in testing the equations to see if the given unknowns work. 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. Simultaneous equations • That example worked. Let’s try another. Example Look at the simultaneous equations below. Check whether and work for these equations. As you can see, this pair didn’t work. Try the worksheets!

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