Question

Which of these describes the system of linear equations below? 3x - 2y = 7 6x - 4y = 14 The system has no solutions. The system has infinitely many solutions. The ratio of the x-coordinate to the y-coordinate of the only solution is 2:1. The difference between the x-coordinate and y-coordinate of the only solution is one.

Answer 1

We have two linear equations

3x - 2y = 7 -------- equation 1

6x - 4y = 14 -------- equation 2

These system linear equations can be solve simultaneously either by using the elimination method or substitution method

Let us try the elimination method

3x - 2y = 7

6x - 4y = 14

Firstly, let us eliminate x

To eliminate x , we need to make the value of x equal in both equations

To make the value of x equal, mulitply equation 1 by 2 and equation 2 by 1

3x * 2 - 2y * 2 = 7 x 2

6x * 1 - 4y * 1 = 14 x 1

6x - 4y = 14 -------- equation 3

6x - 4y = 14 ------- equation 4

To eliminate x, substract equation 4 from 3

6x - 6x -4y -(-4y) = 14 - 14

6x - 6x -4y + 4y = 14 - 14

0 - 0 = 0

0 = 0

From the above explanation, we can conclude that the system linear equations does not have a solution

The answer is OPTION A