Question

How many solutions does this system have?

2x-4y=8
x+y=7
The system has ______
solution(s)

Answer 1

The solution for the system is the pair (6,1).

Explanation:

The system has two equations and two variables, therefore i has only one solution. To solve it we will multiply the second equation by "-2". So we have:

2x-4y = 8

x + y = 7 *(-2)

2x - 4y = 8

-2x -2y = -14

We now sum boh equations:

2x -2x -4y -2y = 8 -14

-6y = -6

y = -6/-6 = 1

2x - 4(1) = 8

2x - 4 = 8

2x = 8 + 4

2x = 12

x = 12/2 = 6

The solution is the pair (6,1).

Answer 2

The system has 2 solution .

Explanation:

The equation is a simultaneous equation

2x - 4y=8 ............(i)

x + y=7................(ii)

make x the subject of the formula in equation (ii)

x = 7 - y

Substitute the value of x in equation(i)

2(7 - y) - 4y = 8

14 - 2y - 4y = 8

14 - 6y = 8

-6y = 8 - 14

-6y = -6

divide both sides by -6

y = 1

insert the value of in equation (ii)

x + y = 7

x + 1 = 7

x = 7 - 1

x = 6

The system has 2 solution .