Question

To solve the system of linear equations 3x+5y=2 and 6x+10y=8 by using the linear combination method, Laura correctly multiplied the first equation by –2 to get -6x-10y=-4 and then correctly added the equations -6x-10y=-4 and and then correctly added the equations -6x-10y=-4 and 6x+10y=8 to get 0 = 4. How many solutions are there to the system of equations?

A. 0
B. 1
C. 2
D. 4

Answer 1

The answer is A, those linear lines will never intersect

Answer 2

The two linear equation are

1. 3 x + 5 y =2

2. 6 x + 10 y = 8

If you will multiply equation (1), by number ,2 you will get

6 x + 10 y=4

or, if you will divide equation 2,by 2 you will get ,line

2 × (3 x + 5 y)=2 × 4

3 x + 5 y=4

→Slope of line 1

`=(-3)/(5)`

→Slope of line 2

`=(-6)/(10)=(-3)/(5)`

→→Slope of two lines are equal , so they are parallel.

Parallel lines never intersect. So,there is no solution.

Option A: 0