CODEWITHSUNDEEP
wolfram-mathematica
user2966581
user2966581

Reputation:

How to solve an equation system in Mathematica 9

Got a simple equation but Mathematica just can't get it:

Solve[{Sin[x] == y, x + y == 5}, {x, y}]

Error: this system cannot be solved with the methods available to Solve

Am I using the right function? If not, what should I use?

Upvotes: 2

Views: 2566

Answers (1)

Code Different
Code Different

Reputation: 93151

Mathematica knows a lot, but it surely doesn't know everything about math. When stuffs breakdown, you can try a few different approaches:

First let's graph it:

ContourPlot[{Sin[x] == y, x + y == 5}, {x, -10, 10}, {y, -10, 10}]

contour plot

It's a line intersecting a sinusoidal wave and it looks likes there is only one solution. The point is close to (5,0) so let's use the Newton method to find the root:

FindRoot[{Sin[x] == y, x + y == 5}, {x, 5}, {y, 0}]

This gives the answer {x -> 5.61756, y -> -0.617555}. You can verify it by replacing x and y in the equation with the values provided in the solution: 

{Sin[x] == y, x + y == 5} /. {x -> 5.6175550052727`,y -> -0.6175550052726998`}

That gives {True,True} so the solution is correct. Interestingly, as another commenter pointed out, Wolfram Alpha gives the same solution when you type in this:

solve Sin[x]==y,x+y==5

You can access Wolfram Alpha directly from Mathematica by typing == at the beginning of a new line.

Upvotes: 4

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