<p>I just learned a very helpful tip for the SAT math section. I guess you can subtract whole equations from one another to find a variable. here an example question would be: "find y, 2x+z=2y and 2x+2y+z=20." I dont know if this is algebra 1, algebra 2 or if its trig, but i dont seem to remember learning it. Can someone refresh and tell me some rules about when I can or cant use this method? I know I can use it from this equation, but what would an equation where I cant use it look like? Also how do I know which formula to subtract from, and which formula to subtract by? I dont want to use this method on the wrong types of questions on the SAT! thanks for any help.</p>
<p>You can do it for all problems, but sometimes it may not lead you to a solution and other times you have to be a bit clever. The rules are pretty basic. If A = B, and C = D, then A-C = B-D, and A+C = B+D. You can generalize it and say pA + qB = pC + qD for constants p,q.</p>
<p>Here is an example problem:
If a+b+c = 10 and 2a+2b-c = 3, find c.</p>
<p>It’s practically the same thing as linear combination/elimination, which you should have learned in Algebra I. (If you don’t remember it, you were likely pushed down the path of substitution. Substitution is ‘more correct’ but it’s not always easier.)</p>
<p>@MITer94, is this a non sequitur? If not, how is it a generalization?</p>
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<p>Maybe you meant pA + qC = pB + qD?</p>
<p>This is simply the elimination method. You should have learned it in Algebra I. It can be used for solving most systems of equations. This is essentially the same thing as matrix manipulation if you’ve had any experience with matrices. You can also take multiples of a given row and add/subtract them to another row to eliminate variables. If you want to know more about it you should be able to find some good videos on it on Khan Academy. </p>
<p>@ItsJustSchool Yeah sorry, that’s what I meant (I don’t always think/proofread while typing)…thanks for catching that.</p>
<p>And yes, pA + qC = pB + qD follows. A = B implies pA = pB, similarly C = D implies qC = qD for all constants p, q (note that converse is not necessarily true). Then combining these two statements implies pA + qC = pB + qD.</p>
<p>The main point is, given a set of equations, you can add/subtract a linear multiple of one from another to obtain a true statement.</p>