How Do I Solve Linear Equations with Fractions and Word Problems in Algebra?

[MATH DUMMY]

5X-5/2Y=-55
4X+2Y=-12
USE ADDITION METHOD...HOW I DO THIS PROBLEM THE FRACTIONS THROW ME OFF

ALSO
A VENDOR SELLS HOT DOGS AND BAGS OF CHIPS.A CUSTOMER BUYS 2 HOT DOGS AND 2 BAGS OF CHIPS FOR $7.00.ANOTHER CUSTOMER BUYS 4 HOT DOGS AND 5 BAGS OF CHIPS FOR $15.00.FIND THE COST OF EACH ITEM.

SOLVE:THE ANWSER IS $2.50 HOT DOGS AND CHIPS $1.00.

4x+3y=$12.25
2x+5y=$8.75
IS THAT HOW I SHOULD SET IT UP.THEN WHAT I DO?...SORRY MY NAME GOES PERFECT WITH THIS PROBLEM

 

[Quadratic]

5X-5/2Y=-55
4X+2Y=-12

You can just solve this by substitution. From the second equation:

4x+2y=-12
4x=-2y-12
2x=-y-6
y=(-2x-6)

So, you substitute that value in for y, and you get:

5x-(5/2)(-2x-6)=-55
5x-(-5x-15)=55
5x+5x+15=55
10x=40
x=4

Then, we replace x with 4, which gives us:

4(4)+2y=-12
16+12+2y=0
2y=-28
y=-14

So, x=4 and y=-14

ALSO
A VENDOR SELLS HOT DOGS AND BAGS OF CHIPS.A CUSTOMER BUYS 2 HOT DOGS AND 2 BAGS OF CHIPS FOR $7.00.ANOTHER CUSTOMER BUYS 4 HOT DOGS AND 5 BAGS OF CHIPS FOR $15.00.FIND THE COST OF EACH ITEM.

SOLVE:THE ANWSER IS $2.50 HOT DOGS AND CHIPS $1.00.

Correct.

4x+3y=$12.25
2x+5y=$8.75

Again, this is called "solving a system of equations". You can use all sorts of methods to solve this, including solvin by substitution (which I used for the first question), elimination (trying to combine the equations, making one variable cancel), and even matricies. I might elaborate in a bit, but I'm getting increasingly sleepy...

 

[Architeuthis Dux]

I am not an expert in solving word problems involving addition and fractions. However, I can provide some guidance on how to approach these types of problems.

For the first problem, the best method to use would be the addition method. This involves adding or subtracting the equations to eliminate one of the variables. In this case, we can add the two equations together to eliminate the y variable.

(5x-5/2y) + (4x+2y) = -55 + (-12)

9x = -67

x = -7.44

To find the value of y, we can substitute x=-7.44 into one of the original equations and solve for y.

5(-7.44) - 5/2y = -55

-37.2 - 5/2y = -55

-5/2y = -17.8

y = 7.12

So the solution to this problem is x=-7.44 and y=7.12.

For the second problem, we can set up a system of equations:

2x + 2y = 7
4x + 5y = 15

To solve this, we can use the elimination method by multiplying the first equation by -2 and adding it to the second equation to eliminate the x variable.

-4x - 4y = -14
4x + 5y = 15
-------------------
y = 1

Substituting y=1 into the first equation, we can solve for x.

2x + 2(1) = 7
2x = 5
x = 2.50

Therefore, the cost of hot dogs is $2.50 and the cost of chips is $1.00.

I hope this helps and good luck with your word problems!