Question

Solve for x and y:

28x−49y=35
4x−7y=5
Select one:
a. The solution is (0, 0).
b. There are an infinite number of solutions.
c. There is no solution.
d. x=3,y=1

Answer 1

Write the given equations as follows:
28x - 49y = 35 (1)
4x - 7y = 5 (2)

Divide equation (1) by 7 to obtain
4x - 7y = 5

This equation is identical to equation (2).
This means that we are trying to determine values for x and y (2 variables) from one equation. There will be an infinite number of solutions.

Write the one equation as
7y = 4x - 5
or
y = (4x - 5)/7

For any value of x, a corresponding value can be obtained.
Because we may choose x to be any real number from an infinite set, there will be a correspondingly infinite number of y values.

Answer: b.
There are an infinite number of solutions.

Answer 2

The system:
28 x - 49 y = 35
4 x - 7 y = 5 / * ( - 7 ) / we will multiply both sides by - 7 /
----------------------
28 x - 49 y = 35
+
- 28 x + 49 y = - 35
---------------------------
0 * x + 0 * y = 0,
0 = 0 x, y ∈ R
Answer: b. There are infinite number of solutions.