two records and three tapes cost $31.three records and two tapes cost $29.find the total cost of each record and each tape

2R + 3T = 31

3R + 2T = 29

multiply the first by 2, and the second by 3, then subtract. That will allow you to find R. Sub it back into either of the two equations.

From the first statement, 2r + 3t = 31.

From the second statement, 3r + 2t = 29.

What do you have to do to make the coefficients of one of the variables be equal?

Having satified that requirement, what can you nopw do to eliminate one of the variables and solve for the other?

To solve this problem, let's assume the cost of each record is "R" and the cost of each tape is "T". We need to find the values of R and T that satisfy both equations.

Let's write the given information as two equations:

Equation 1: 2R + 3T = 31 (two records and three tapes cost $31)
Equation 2: 3R + 2T = 29 (three records and two tapes cost $29)

To solve these equations, we can use either substitution or elimination method. Here, we will use the elimination method.

Step 1: Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of R the same:
6R + 9T = 93 (equation 1)
6R + 4T = 58 (equation 2)

Step 2: Subtract equation 2 from equation 1 to eliminate R:
(6R - 6R) + (9T - 4T) = (93 - 58)
5T = 35

Step 3: Divide both sides of the equation by 5 to solve for T:
T = 7

Step 4: Substitute the value of T back into one of the original equations to solve for R. Let's use equation 1:
2R + 3(7) = 31
2R + 21 = 31
2R = 31 - 21
2R = 10
R = 5

Therefore, the cost of each record (R) is $5, and the cost of each tape (T) is $7.