Question

Solve the system of equations algebraically:

c + d = 5
2c - d = 3

a) c = 2, d = 3
b) c = 3, d = 2
c) c = 4, d = 1
d) c = 1, d = 4

Answer 1

To solve the given system of equations c + d = 5 and 2c - d = 3 algebraically, you can use the method of substitution or elimination. Using the substitution method, the solution is c = 8/3 and d = 7/3.

Step-by-step explanation:

To solve the given system of equations algebraically, we can use the method of substitution or elimination. Let's use substitution method:

Step 1: Solve the first equation for one variable in terms of the other. Here we solve for d:

c + d = 5

d = 5 - c

Step 2: Substitute the expression for the variable found in step 1 into the second equation:

2c - (5 - c) = 3

3c - 5 = 3

Step 3: Solve for the remaining variable:

3c = 3 + 5

3c = 8

c = 8/3

Step 4: Substitute the value found for c into one of the original equations and solve for the other variable:

d = 5 - c = 5 - (8/3)

d = 15/3 - 8/3

d = 7/3

Therefore, the solution to the given system of equations is c = 8/3 and d = 7/3.