How do you solve the following system of equations?: #x2y=13 , x  y= 10#?
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To solve the system of equations (x  2y = 13) and (x  y = 10), you can use the method of substitution or elimination. Here's how you can solve it using the substitution method:

Solve one of the equations for one variable in terms of the other. Let's solve (x  y = 10) for (x): (x = y + 10).

Substitute the expression found in step 1 into the other equation. Substitute (x = y + 10) into (x  2y = 13): ((y + 10)  2y = 13).

Solve the resulting equation for the variable. Expand and simplify: (y + 10  2y = 13) becomes (10  y = 13). Rearrange and solve for (y): (10  13 = y) implies (y = 3).

Once you have found the value of one variable, substitute it back into one of the original equations to solve for the other variable. Substitute (y = 3) into (x  y = 10): (x  (3) = 10). Simplify: (x + 3 = 10). Solve for (x): (x = 7).
So, the solution to the system of equations is (x = 7) and (y = 3).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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