Question

Consider the following system of equations.

1.75x + 1.25y = 2.75
7x + 5y = 9
What is the solution to the system?
Choose the correct response.
A. Since 11 ≠ 9, there is no solution.
B. Since 0 = 0, there are infinitely many solutions.
C. There is one solution, x = 0 and y = 0.
D. There are two solutions, the points (11, 0) and (0, 9).

Answer 1

Explanation:

1.75x + 1.25y = 2.75 (1)

7x + 5y = 9 (2)

On multiplying EQ. 1 by 4

4(1.75x + 1.25y) = 4(2.75)

7x + 5y = 11 (3)

We get the same LHS as equation 2 but not same RHS as equation 2

Option A is correct

Answer 2

• A. Since 11 ≠ 9, there is no solution

Explanation:

Given system:

• 1.75x + 1.25y = 2.75
• 7x + 5y = 9

Multiply the first equation by 4:

• 4(1.75)x + 4(1.25)y = 4(2.75)
• 7x + 5y = 11

We get same equation as the second one with the difference that the right side equals to 11.

Since left sides are same and right sides are different, the system has no solution.

Correct choice is A