<p>SAT questions often ask you to not solve for x, but instead for x+y or (x+y)^2...Is it possible to use the TI 89 calculator to solve for x+y as opposed to solely x?</p>
<p>I don’t have my ti89 w/ me to check if this would work, but if I did, here’s what i would try: make a new variable and add a new equation to the system – so say z=x+y, seprate it from the other two eqns with “and” and then try solving for z. But again, I have not tried this…</p>
<p>On the other hand, when they ask you to solve for “x+y” rather than say just x, there’s a reason. Stop and THINK and I bet you can find the solution faster without a calculator.</p>
<p>For example, try this one:</p>
<p>Given that x^2 + y^2 = 30 and xy=3, find one possible value of x+y.</p>
<p>This COULD be done with ti89, but there’s a much faster way…</p>
<p>Yeah, you probably could, but that’s a waste of time and effort.</p>
<p>Every SAT question that asks you to solve for something like that by giving you two different expressions or something can be solved really quickly. Using the example pckeller gave up there, think about (x+y)(x+y). That expands to x2 + 2xy + y2. rearrange that, you have x2 + y2 = 30, and 2xy = 2(3) = 6. So x2 + 2xy + y2 = 36. Factor that back to (x+y)(x+y). (x+y)^2 = 36. Take the square root, bam, your answer is + or - 6. Probably positive 6 on the SAT. All in all, that should take no more than 10 seconds to do. Much quicker and more effective than using your calculator.</p>
<p>OK, for the record:</p>
<p>Solve(x^2+y^2 = 30 and x*y=3 and z=x+y,{x,y,z})</p>
<p>successfully generates all four real solutions. So the ti89 is pretty amazing…but that’s STILL not the best way…</p>
<p>AKShockwave does it right…</p>
<p>I realize there is a way to solve given questions like that and I am generally able to find the method but as I complete Barron’s math level 2 tests there are around 2 problems that end of stumping me. I prepared well for those problems for sat math 1 but for some reason barrons seems to stump me…</p>
<p>and I disagree…I find on the sat math tests I am scrambling to complete everything and my work often gets jumbled (too rushed to be organized)…the calculator is neat, organized, you can easily check your work and there is no human error. I think knowing how to solve problems like these via calculator is far more efficient.</p>
<p>You can solve for x+y by defining a new variable (e.g. z = x+y) and trying to rework everything in terms of z. However, if you find yourself in this position, you may want to see if there’s an easier solution. Consider the following questions:</p>
<ol>
<li><p>x and y are real numbers such that x^2 + y^2 = 30 and x^3 + y^3 = 100. Find a possible value for x+y.</p></li>
<li><p>x and y are positive real numbers with (1/x) + (1/y) = 10. Find the range of all possible values for x+y.</p></li>
</ol>
<p>These aren’t SAT-level (I intentionally made up harder questions to provide examples of more abstract Q’s that may or may not require the TI-89 solution).</p>
<p>I’ll let you take a look at these. I worked them out: One of these does not require a calculator whatsoever, and a calculator may be useful for the other one.</p>