Is this true?The substitution method is sometimes easier to use than the addition method.?

Answer 1

Yes, if one or both equations already has one of the variables isolated, it's very easy to plug that variable into the other. that's why it's good to have several methods available.

For example

y = 2x
3x + 4y = 24

It's a lot easier to plug the fist equation into the second than to translate the first into standard form and use the addition method.

Another nice thing about the substitution method is that it's a lot more versatile, you can solve various types of equatios with it. For example, a system of a linear and a quadratic, or a system of a quadratic and an exponential. With the addition method the equatios have to be both of the same order.

Answer 2

My selection will be to multiply the first equation with the help of four and subtract the words of the 2d from the first, thereby eliminating x. Then make certain for y and finally use the outcome for y to make certain x. Like so: -2x + 4y = 7 (a million) -8x - 9y = 3 (2) Multiply Eq (a million) with the help of four: -8x +16y = 28 (3) -8x - 9y = 3 (2) Subtract Eq(2) from Eq(3): 0x + 25y = 25 => y = a million change in a million for y into Eq(a million) say. -2x + 4 = 7 -2x = 3 => x = -3/2 once you're wondering why I labelled -8x + 16 = 28 Eq(3), that's basically to pastime my memory that I have worked on Equation1. frequently it facilitates me to save music of any artwork I have made in my calculations.

Answer 3

Yup. Let's compare by doing a sample problem:

Substitution Method:

y=7x
5x + 2y = 19

5x + 2(7x) = 19
5x + 14x = 19
19x = 19
x = 1

y = 7x
y = 7(1)
y = 7

Solution: (1,7)
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Elimination Method:

y=7x
5x + 2y = 19

7x - y = 0
5x + 2y = 19

2(7x - y = 0)
5x + 2y = 19

14x - 2y = 0
5x + 2y = 19
-----------------
19x = 19
x = 1

y = 7x
y = 7(1)
y = 7

Solution: (1,7)
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It's a little less work solving this particular problem using substitution. Think of the different methods as tools. You don't necessarily want to use the same tool for every job. As you gain more practice and experience solving systems, you'll be able to more easily choose the most efficient tool for the job.

Hope this helps! :)

Answer 4

Yes and I will show you an example:
y=2x
4x+y=12

4x+2x=12
6x=12
x=2

4(2)+y=12
8+y=12
y=4

The solution set is (2,4)

Check:
4=2(2)
4=4

4(2)+4=12
8+4=12
12=12

I hope that helps!

Answer 5

Yes. Pariticularly for the intersections of lines & curves.

Answer 6

yes probably

x = 17y
33x + 2727y=17

here it is easier to substitute ( easier for me )

Answer 7

yes

Answer 8

yes!