Unit 5 - Simultaneous Equations

Question 1

What is a simultaneous equation

Answer 1

• Occurs when a set of equations has a set of values (x, y) that satisfies both
  equations

Simply: it means that you’re looking for one pair of values for 𝑥 and 𝑦 that works in both equations at once.

Question 2

What is a solution

Answer 2

Solution:
- The set of values that satisfies both equations
- Also referred to as the point of intersection

• As simultaneous equations can be referred as lines, you can have: intersecting lines (one solution), parallel lines (no solution), or coincident lines [on top of each other] (infinite solutions)

Question 3

How to solve simultaneous equations graphically?

Answer 3

Step 0: Rearrangement if necessary: y = ____ x + ______

Step 1: Plot lines on same axis (grid)

Step 2: Graph on the axes

Step 3: Determine the point of intersection (if any)

Step 4: Checking your work:
Substitute the solution into both equations to check your answer

*However, it is not always easy to see where the point is, in these cases, use your graphing calculator

Question 4

How to solve simultaneous equations on a calculator?

Answer 4

To graph them:
1) After turning it on and clearing your memory
2) Access the equations input function located in
the TOP LEFT of your calculator ( y = …)
3) Here, you will input your first equation under y1 = …
4) Here, you will input your second equation under y2 = …
5) Click the graph button

To find the intersection:
6) To find the “Point Of Intersection” (POI), you will need to click the (2nd) (Trace) buttons in that order
7)You will need to choose 5: Intersect
8) Click enter three times
9) Now it shows the intersection

Question 5

Solving Algebraically - Equating Values of Y

Answer 5

Equating values of y only works when:
- The system contains 2 equations in which y is the subject for both
- When this happens, we equate the y values and solve for x

*Basically, for both;
1. if they start with (y=…), then take what they are equal to, and make them equal to one another to solve for X
2. Take the value for X, and plug back into one of the formula’s to solve for Y

Question 6

Solving Algebraically - Substitution

Answer 6

• Used when at least one equation is given with either x or y as the subject of the formula (without a coefficient)
• Substitute an expression (after equals sign) for this variable into the other formula

Question 7

Solving Algebraically - Elimination

Answer 7

• Used when either equation does not have just x or y as the subject (so substitution is lots of work to rearrange)
• Make the coefficients (x or y) the same size. We then add or subtract, thereby eliminating one of the variables

*Can also multiply one or both equations if necessary

Question 8

How to solve word problems?

Answer 8

1. Decide on the unknowns x and y, don’t forget units
2. Write down two equations connecting x and y
3. Solve the equations simultaneously
4. Check solutions with original data given
5. Write answers in sentance form