Stumped by Substitution

[EandH]

I don't know how to carry out these substitution problems. None of my practice problems every look anything like the simple addition examples they give...Here's what I have so far...

x+8y = 8
9x-5y= -5
9x-5y(x+8y)=-5
9x-40y=-5 - what next?

 

[mmm4444bot]

?

x + 8y = 8

9x - 5y = -5

9x - 5y (x+8y) = -5 This is not a substitution; you "inserted", instead, which is not allowed.

We call the two given equations a "system of two equations".

To solve such a system using the Substitution Method requires first solving one of these two equations (your choice) for one of the variables x or y (again, your choice).

We then substitute the result for the same variable in the other equation.

Here's one choice: Solve the first equation for x, and then replace x in the second equation with the result.

I'll show how it works, using a similar example.



x - 4y = 30

4x - 3y = 29

We will solve this system of two equations using the Substitution Method.

We have a choice, and we decide to solve the first equation for x, and then substitute the result for x in the second equation.

STEP #1: Solve the first equation for x by adding 4y to both sides.

x - 4y + 4y = 30 + 4y

x = 4y + 30

Now that we know the expression 4y+30 is the same as x, we can replace the symbol x with the expression 4y+30.

STEP #2: Substitute 4y + 30 for x in the second equation.

4x - 3y = 29

4(4y + 30) - 3y = 29

Does this make sense, so far? If you're confused, please ask specific questions.

Now we have a new equation that contains only one variable: y. Therefore, we can solve this equation for y.

STEP #3: Solve the new equation, to find that y = -7.

Now that we know the value of y, we can go back to any equation with both x and y, to determine x.

STEP #4: Substitute -7 for y, and solve for x.

x = 4y + 30

x = 4(-7) + 30

So, the solution is x = 2 and y = -7.



Questions about substitution?

If not, then show us what you come up with.

?

 

[EandH]

okay, well i thought i was with you until I came up with this atrocity.

x+8y=8
9x-5y=-5

x+8y + 8y = 8 + 8y
x+16y=8+8y
8x+16y/8 = 16y/8
x+2y/2 = 2y/2
x+y=y????
what on earth...?

 

[Denis]

I can't follow your HOW, but x + y = y means x = y - y, so x = 0.

Did your teacher not show you HOW to do this CLEARLY?

 

[mmm4444bot]

?

x + 8y = 8

x + 8y + 8y = 8 + 8y If you are trying to solve the first equation for x, do not add 8y to both sides.

In order to get x all by itself on the LHS (lefthand side) of the equation, you need to get rid of the 8y term.

Get rid of it by subtraction, not addition.

In other words, subtract 8y from both sides.

After you solve the first equation for x, substitute the resulting expression into the second equation, as shown in blue, in my example.

?

 

[EandH]

okay, i'll try again. My class is online so its more of a self-teaching kind of thing, with teacher as more of a guide. I kind of need things spelled out when it comes to math.

 

[mmm4444bot]

My class is online so its more of a self-teaching kind of thing

My first suggestion is: drop the on-line math courses, and go to a community-college campus.

If this is not an option, for you, then my second suggestion is: seek out local tutoring resources, where you can meet face-to-face, regularly.

Since you struggle to solve a simple linear equation, it's clear that the machine has not adequately prepared you to solve multiple equations at once. I think that you need human teachers.