Linear Equation - Request to Check My Work

[dclary]

Hello. I was wondering if someone would be so kind as to check my work on some linear equations. I have been out of high school for 20 years and some of this algebra stuff is new to me. Through my class, I think I am beginning to get a handle on it but would appreciate if someone could double check me and provide guidance if there is something wrong. There are 3 questions, however, question 1 has parts (a),(b),(c) and (d); question 2 has parts (a)(b) and question 3 is just a word problem. Below is my completed work and thank you in advance for any help.

1. Determine how many solutions exist for the following systems of linear equations (20 points).

(a) 5x + 3y = 8
4x + 15y = 19

Because a1/a2 does not match b1/b2 this is considered unique system.

(b) -x/4 + 3y = 8
(-5/4)x + 15y = 19

Because a1/a2 = b1/b2 but not c1/c2 this system has no solution

(c) 3y = 8
-x + 15y = 19

Because a1/a2 does not match b1/b2 this is considered unique system.

(d) 6x + 4y = 32
3x + 2y = 16

Because a1/a2 = b1/b2 = c1/c2 this system is infinite.

2. Solve the following systems of linear equations (20 points).

(a) -3x + 6y = 2
2x + (2/3) y = 1

(b) (x/3) + (y/4) = 7
(x/4) + (y/3) = 7

3. If I buy two shirts and a pant, it cost me $65. If I buy 3 pants and one shirt it cost me $95. Find the price of a shirt and the price of a pant (9 points).

2x+y = 65
3x+y = 95

x = (65 - y)/2

3(65+y)/2+y = 95

(-1)y = -5

y = 5

x = (65-y)/2

x = 30

 

[Mrspi]

Hello. I was wondering if someone would be so kind as to check my work on some linear equations. I have been out of high school for 20 years and some of this algebra stuff is new to me. Through my class, I think I am beginning to get a handle on it but would appreciate if someone could double check me and provide guidance if there is something wrong. There are 3 questions, however, question 1 has parts (a),(b),(c) and (d); question 2 has parts (a)(b) and question 3 is just a word problem. Below is my completed work and thank you in advance for any help.

1. Determine how many solutions exist for the following systems of linear equations (20 points).

(a) 5x + 3y = 8
4x + 15y = 19

Because a1/a2 does not match b1/b2 this is considered unique system.

(b) -x/4 + 3y = 8
(-5/4)x + 15y = 19

Because a1/a2 = b1/b2 but not c1/c2 this system has no solution

(c) 3y = 8
-x + 15y = 19

Because a1/a2 does not match b1/b2 this is considered unique system.

(d) 6x + 4y = 32
3x + 2y = 16

Because a1/a2 = b1/b2 = c1/c2 this system is infinite.

2. Solve the following systems of linear equations (20 points).

(a) -3x + 6y = 2
2x + (2/3) y = 1

(b) (x/3) + (y/4) = 7
(x/4) + (y/3) = 7

3. If I buy two shirts and a pant, it cost me $65. If I buy 3 pants and one shirt it cost me $95. Find the price of a shirt and the price of a pant (9 points).

2x+y = 65
3x+y = 95

x = (65 - y)/2

3(65+y)/2+y = 95

(-1)y = -5

y = 5

x = (65-y)/2

x = 30

The first group of problems looks fine.

Your solution to the "word problem" is incorrect...

The very first step in this kind of problem is to NAME THINGS. In other words, tell what your variables are going to represent. You didn't do that, and as a result, your equations are not correct.

There are two things you don't know...the price of a shirt, and the price of a pair of pants.

I might have chosen these variables:

Let s = price of a shirt
Let p = price of a pair of pants

Now that you have variables to represent each of the unknowns, see if you can translate the facts of the problem into equations.

The first fact is this:

Two shirts and a pair of pants cost $65.

If s is the price of one shirt, then the price of two shirts will be 2s. And p is the price of one pair of pants. So,

"two shirts and a pair of pants cost $65" translates to
2s + p = 65

The second fact is this:

Three pairs of pants and one shirt cost $95.

one shirt and three pairs of pants cost $95
s + 3p = 95

Ok...now you have TWO equations in two variables....

2s + p = 65
s + 3p = 95

Solve the system. REMEMBER (ALWAYS REMEMBER THIS) to check your solution with the facts of the problem. If you try checking the solution you got, you'll find that it does not satisfy the conditions of the problem.

 

[dclary]

Thank you so much, I really appreciate that you took the time to look this over. As you can tell, I'm not very good with word problems. I have worked it out (see below) and this is what I come up with, it fits the equation so hopefully it is correct now.

2s + p = 65
s + 3p = 95

p = -2x + 65
s + 3(-2x + 65) = 95

s - 6s + 195 = 95
5s + 195 = 95
-5s = -195 + 95
-5s = -100
s = 20

p = -2(20) + 65
p = -40 + 65
p = 25

Check to make sure it works:

2(20) + 25 = 65
20 + 3(25) = 95

Thank you once again