Algebra
Simultaneous Equations
Simultaneous equation items are based on the premise that seeing not just one but two equations causes your brain to leap out of your skull and go cower under a rock. This should be avoided, so let’s review.
You will have two equations that contain two of the same variables:
Two equations, two variables (c and d), and two methods you can use to solve them:
Method 1: Take one equation and solve for one variable in terms of the other, then plug that into the second equation.
We’ll take the first equation, solve for d, then plug that into the second equation.
Notice that we did a little distributing in there, along with all the arithmetic manipulation. Once you have a value for c, you can plug that back into the equation that isolated d.
Method 1 can take some time, but it always works. Method 2 requires a little bit of planning, but it can save you time, so see whether you like it. The key is to answer items correctly, so choose the method with which you are most comfortable.
Method 2: Add or subtract one equation from the other to eliminate one of the variables.
Figuring out how to do this sometimes takes a little manipulating. Look at the two equations again
If you take the first equation and multiply both sides by –2, you have:
The new first equation c term, –4c, would now cancel the c term in the second equation, 4c, if you were to add the equations together. Let’s do just that, then:
Once you have a value for d, you can plug it back into any of the above equations to find the value for c, which will once again be 14.
If you set up the equations right, Method 2 can be a bit faster. That’s why you should spend a moment viewing both equations to see whether you can figure out a way to cancel out one term. If you can, proceed with Method 2. If you can’t, don’t waste more time. Just go with reliable Method 1.
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