Question

Two lines, R and M, are represented by the following equations:
Line R: 2x + 2y = 18
Line M: x + y = 9

Which statement is true about the solution to the set of equations?

It is (18, 9).
It is (9, 18).
There are infinitely many solutions.
There is no solution. (i know it's not this one)

Answer 1

Line R 
2x + 2y = 18
if we divide by 2 in both side
x + y = 9

Line M
x + y = 9

if x = 1, then y = 8
if x = 2, then y = 7

likewise you can find infinite pair answers for x and y

Answer 2

Answer:  The correct option is (C) infinitely many solutions.

Step-by-step explanation:  The representations of two lines 'R' and 'M' are given by

$\textup{Line R: }2x+2y=18~~~~~~~~~~~~~~~~~~~~(i)\\\textup{Line M: }x+y=9~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We are to select the TRUE statement about the solution to the above set of equations.

Multiplying equation (ii) by 2, we have

$\textup{Line M: }2x+2y=18~~~~~~~~~~~~~~~~~~~(iii)$

From equations (i) and (iii), we can conclude that

the equations for line 'R' and line 'M' are same, and hence their graph is the same straight line as shown in the attached figure.

Therefore, each point on the lines is a solution to the given system, because both the lines intersect at each and every point that lies on the lines.

For example, (0, 9), (9, 0), (4, 5), etc. are solutions to the system.

Thus, there are infinitely many solutions.

Option (C) is correct.