How to solve systems of equations, Mathematics

Assignment Help:

How to solve Systems of Equations ?

There's a simple method that you can use to solve most of the systems of equations you'll encounter in Calculus. It's called the "substitution method."

This is not the only method - and often, it's not the easiest either. But it's something you can usually fall back on when other things don't work. It's also the easiest to learn, in case you've been having trouble learning other methods.

Step 1. Solve one of the equations for one of the variables.
Step 2. By substitution, eliminate that variable from the other equations.

Now you have fewer equations, and fewer variables . Repeat steps 1 and 2 until you have only one equation and one variable.

Step 3. Solve that equation with one variable. Now you know the value of that one variable.
Step 4. Go back to the other solved equations to find values for the other variables.
Step 5. Check your work!

To demonstrate, let's solve this system of equations:

x2 + y = 3 (2a)

15x + 3y = 21 (2b)

Let's solve equation (2a) for y (Step 1).

y = 3 - x2

Since y is equal to 3 - x2 , we can substitute 3 - x2 for y wherever y occurs. Let's make this substitution in equation (2b) (Step 2):

15x + 3(3 - x2 ) = 21.

Notice what we've accomplished: we have an equation with only one variable in it. Now we solve for that variable (Step 3):

15x + 9 - 3x2 = 21

-3x2 + 15x - 12 = 0

-3(x2 - 5x + 4) = 0

-3(x - 4)(x - 1) = 0

x = 4 or x = 1.

Now, Step 4: use these values for x to solve (2a) for the other variable y:

x2 + y = 3

(4) 2 + y = 3 or (1) 2 + y = 3

16 + y = 3 or 1 + y = 3

y = -13 or y = 2.

So, the possible solutions are

A. x = 4, y = -13

B. x = 1, y = 2.

Often these are written simply as (4, -13) and (1, 2).

Step 5: Check these solutions with the original equations (2a) and (2b). For example, let's check the possible solution (4, -13) with equation (2a):

x2 + y = 3

(4)2 + (- 13) = 3

16 - 13 = 3

which is true. You can do the rest of the checks yourself.


Related Discussions:- How to solve systems of equations

Muptipucation, if 2+2=4 what does two times two epual?

if 2+2=4 what does two times two epual?

What is negative exponents explain, What is Negative Exponents explain? ...

What is Negative Exponents explain? Here's a problem which results in a negative exponent: 3 4 /3 7 = 3 (4-7) = 3 -3 A negative exponent means the same thing as making

..Job, Eddie mkes $15.75 per hour. Estimate how much Eddie will make per ye...

Eddie mkes $15.75 per hour. Estimate how much Eddie will make per year if he works 40 hours per week and 50 weeks per year.

Straight Line, can i known the all equations under this lesson with explana...

can i known the all equations under this lesson with explanations n examples. please..

Differential equatoin, how to solve questions based on higher differential ...

how to solve questions based on higher differential equations

Core concepts of marketing, examination questions and answers to the above ...

examination questions and answers to the above title.

Properties of triangle, In triangle ABC, cosecA(sinB.sinC+cosB.sinC) is equ...

In triangle ABC, cosecA(sinB.sinC+cosB.sinC) is equal to..?

Original price of the mittens was $10 what is the new price, A pair of mitt...

A pair of mittens has been discounted 12.5%. The original price of the mittens was $10. What is the new price? Find 12.5% of $10 and subtract it from $10. Find out 12.5% of $10

#change of ratio, #in a picnic the ratio of boys to girls is 3:4. when 6 bo...

#in a picnic the ratio of boys to girls is 3:4. when 6 boys joined the group the ratio became even. how many boys were there before? how many children were there before? how many b

Judgment sampling, Judgment Sampling Here the interviewer chooses whom ...

Judgment Sampling Here the interviewer chooses whom to interview believing that their view is more fundamental because they might be directly affected for illustration, to find

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd