Solving multi step linear equations

Here is an example on linear equations in two variables, hope the steps followed will be helpful for you to solve similar kind of linear equation problems.

Topic : Linear equations

Number with an variable is called as co-efficient of that particular variable.

Problem : Solve 8y – 4 – 7y = 11

Solution :
Step : 1
Subtract the like terms
8y – 7y – 4 = 11
y – 4 = 11

Step : 2
Add 4 on either side of the equation
y – 4 + 4 = 11 + 4
y = 15

So the solution : y = 15

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Question on Integrating a Function to Find a Value

Here is a Multi choice question to Evaluate the value of function by Integration. You can find similar set of questions at TutorVista Blogs.
Topic : Integration of Function.
Below example will help you to identify correct choice and get reasons for, why remaining choices are incorrect.
Question : If ₀∫^xf(t)dt = x Cos Πx, then the value f(4) is
a. 0
b. 1
c. -4Π + 1
d. -3
Solution :
Choice b is correct.
Integration is as follows,
₀∫^xf(t)dt = x Cos Πx
d/dx(₀∫^xf(t)dt) = d/dx (x Cos Πx)
f(x) = x (- Sin Πx). Π + (Cos Πx). 1
f(4) = 4Π (- Sin 4Π) + (Cos 4Π)
= 0 + 1 = 1

Choice a is incorrect because of the error in substituting the value of cos 4Π as 0 instead of 1.

Choice c is incorrect because of the error in substituting the value of sin 4Π as 1 instead of 0.

Choice d is incorrect because of the error in missing Π in the first term and also substituting the value of sin 4Π as 1 instead of 0.

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