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

Magnitude - vector, Magnitude - Vector The magnitude, or length, of th...

Magnitude - Vector The magnitude, or length, of the vector v → = (a1, a2, a3) is given by, ||v → || = √(a 1 2 + a 2 2 + a 2 3 ) Example of Magnitude Illus

Prove the equality of axiom choice, (1) Prove that Zorn's lemma is equivale...

(1) Prove that Zorn's lemma is equivalent to axiom of choice. (2) Use Zorn's Lemma to prove the existence of E.

First order differential equations, In this section we will consider for so...

In this section we will consider for solving first order differential equations. The most common first order differential equation can be written as: dy/dt = f(y,t) As we wil

Math help, What fraction of the full price will you pay for 2 shirts? 3 4 ...

What fraction of the full price will you pay for 2 shirts? 3 4 11 2 $45.001 2 .

Other ways to aid learning maths, OTHER WAYS TO AID LEARNING :  Here we sh...

OTHER WAYS TO AID LEARNING :  Here we shall pay particular attention to the need for repetition, learning from other children, and utilising errors for learning.

Calculate the area of the ade and compare it with abc, The vertices ...

The vertices of a ? ABC are A(4, 6), B(1. 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that AD/AB = AE/AC = 1/4 .Calculate the  ar

How many ways are there to seat these children, Question: (a) Suppose ...

Question: (a) Suppose that a cookie shop has four different kinds of cookies. Assuming that only the type of cookie, and not the individual cookies or the order in which they

Radius of rhim, how long is the radius of car tyre?

how long is the radius of car tyre?

Fractions rates and ratios, In 6th grade I am learning about ratios rates a...

In 6th grade I am learning about ratios rates and fractions. I am working on vmathlive.com and need serious.

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