Question | Answer |
Simultaneous Equations
Addition/Subtraction/Elimination Method | 1. Multiply one or both equations by some number to make the number in front of one of the variables the same in each equation |
Elimination Method Example | 3x + 3y = 24
2x + y = 13
MULTIPLY bottom equation by -3 |
Elimination Method Example(Card 2) | Equations become:
3x + 3x = 24
-6x - 3y = -39 |
Elimination Method Example (Card 3) | 2. ADD the equations to eliminate the y variable. You get: -3x = -15.
SOLVE for x to get x = 5. |
Elimination Method Example (Card 4) | To solve for y, plug the value x = 5 back into either original equation.
EXAMPLE: 2(5) + y = 13
10 + y = 13
y = 13 - 10, so y = 3. |
Simultaneous Equations
Substitution Method | For this method, you need to isolate one of the variables on one side of the equation |
Substitution Method Example (Card 1) | Let's use the equations
x + y = 3
2x + 3y = 8 |
Substitution Method (Card 2) | In the first equation, move everything but the x to the right side of the equation to get:
x = 3 - y |
Substitution Method (Card 3) | Now wherever there is an x in the second equation, we can substitute
3 - y. So the equation 2x + 3y = 8 becomes 2(3 - y) + 3y = 8. |
Substitution Method (Card 4) | When we simplify this, we get
6 - 2y + 3y = 8.
This becomes 6 + y = 8 or
y = 8 - 6 = 2 |
Substitution Method (Card 5) | Now, to solve for x, simply plug the value for y, which is 2, back into the first equation:
x + 2 = 3. So, x = 1. |