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# Simultaneous Eqns

### Methods and steps for solving algebraic simultaneous equations

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.
Created by: wronawoman