Solving simultaneous equations Flashcards
1
Q
Describe the process in solving simultaneous equations
A
- Make them both have the same amount of x or y
- Eliminate the same x or y’s from the equation. Subtract if they have the same signs (e.g both positive or both negative) but if different signs then add.
- Solve it
- Substitute the answer into the equation to get the other value
2
Q
Example 1 - Solve:
5x-y=16
3x-y=10
A
- The number of y’s is the same, and both have the same sign (minus) so subtract the bottom equation from the top
- This leaves us with 2x=6
- Divide it by 2 to give x=3
- Substitute it into the equation: if x=3, then 5x=15, so if 15-y=16 then y must be 1
- Answers: x=3, y=1
3
Q
Example 2 - Solve:
2x+y=11
3x+2y=18
A
- There is not an equal number of x or y, so we have to make there be an equal number by multiplying. In this case, let’s make y the same by multiplying the top equation by 2. This makes it: 4x+2y=22
- Minus the bottom equation from the top one: x=4
- Substitute x in: if x=4, then 2x=8. 8+y=11, so y=3
- Answers: x=4, y=3
4
Q
Example 3 - Solve:
6x-4y=-2
3x+6y=15
A
- There needs to be an equal number of y or x, so let’s get the number of x’s the same by multiplying the bottom equation by 2. This gives: 6x+12y=30
- Now let’s minus the top equation from the bottom equation. This gives us: 16y=32
- Now divide 32 by 16 to find y. This gives us: y=2
- Substitute y back into the equation so: if y=2, then 6y=12. 3x+12=15.
- This means x must be 1
- Answers: x=1, y=2
5
Q
Example 4 - Solve:
3x+5y=2
y=x+2
A
- If y is equal to x+2, then 3x+5 lots of y is also the same as 3x+5 lots of x+2. We write this in brackets to get: 3x+5(x+2). We are also told 3x+5 lots of y is equal to 2 , so we finish this off by saying: 3x+5(x+2)=2
- Now we expand the brackets: 3x+5x+10=2
- We can add the x values together so: 8x+10=2
- Let’s get rid of the 10: 8x=-8
- Simplify this: x=-1
- Substitute x into the equation, using the bottom line: y=-1+2
- -1+2=1, so y=1
- Answers: y=1, x=-1
