Question

How many solutions does this system have? 2 x minus 4 y = 8. x + y = 7.

Answer 1

Only one solution

Step-by-step explanation:

`2x - 4y = 8 \\ \\ \therefore \: 2(x - 2y) = 8 \\ \\ \therefore \: x - 2y = 4 \\ \\\therefore \: x = 2y + 4 ...(1) \\ \\ x + y = 7...(2) \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ 2y + 4 + y = 7 \\ \\ \therefore \: 3y = 7 - 4 \\ \\ \therefore \: 3y = 3 \\ \\ \therefore \: y = 1 \\ \\ \implies \: x = 2 * 1 + 4 \\ \\ \implies \: x = 2 + 4 \\ \\ \implies \: x = 6 \\ \\ \therefore \: ( x, \: \: y ) = (6, \: \: 1)`

Answer 2

1

Explanation:

There can be 0, 1 or infinitely many solutions. 0 if they are parallel and are different lines, 1 if the slopes are different, and infinitely many if they are the same line.

2x - 4y = 8

x + y = 7

Change to y = mx + b

y = (1/2)x - 2

y = -x + 7

The slopes are different so there is 1 solution.