- 1). Look for similarities between the two equations. This is how you can determine which tactic to use. So, if an equation is
4x - 10y = 2
6x + 10y = 28
then you can use elimination to quickly solve it. You can recognize this by seeing that the equations contain two like terms (10y) that can immediately cancel out. - 2). Eliminate one of the variables by combining the equations, if possible. This is the easiest way to solve simultaneous equations, so if you can do this you should. So, for the example above you can just add them together:
4x-10y+10y+6x=30
The 10y is rendered redundant by the presence of its opposite, and the x values add together. So your equation is now a much more manageable 10x=30, and therefore x=3 - 3). Multiply values to get to a point where you can substitute. So assume that the equations are
2x - 5y = 1
6x + 10y = 28
You can create a manageable equation by multiplying everything in the first one by 2, or dividing everything in the 2nd one by 2. This turns the 5y into 10y and vice versa. Then you can simply follow the elimination method in step 2. - 4). Use substitution to finish solving the equation. So, we know that x=3. Now you need to plug that value into the first equation to find y.
4(3)-10y=2
12-10y=2
-10y=-10
y=1 - 5). Use substitution from the beginning if you cannot eliminate variables. Your first step, then, is to isolate one of the variables in one of the equations. Here we'll isolate "x."
4x-10y=2
4x-10y-2=0
-10y-2=4x
10y+2=4x
2.5y+0.5=x - 6). Plug the equation you've created in Step 5 into the second equation. In this case we're substituting the value we found for x:
6x+10y=28
6(2.5y+0.5)+10y=28
15y+3+10y=28
15y+10y=25
25y=y
y=1 - 7). Plug the y value you found in step 6 back into the original equation to find x.
6x+10(1)=28
6x+10=28
6x=18
x=3
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