How many solutions does the system have x + 4y = 8 \\ x + 2y = 4x + 4y = 8x + 2y = 4a) 0 b) 1 c) 2 d) infinite number

Question

How many solutions does the system have
`x + 4y = 8 \\ x + 2y = 4`x + 4y = 8x + 2y = 4a) 0 b) 1 c) 2 d) infinite number

Answer 1

one solution (option B)

Step-by-step explanation:

x + 4y = 8 ...equation 1

x + 2y = 4 ....equation 2

Using elimination method:

We would be eliminating x as the coefficient of x in both equation is the same.

subtract equation 2 from 1:

x - x + 4y - 2y = 8 - 4

0 + 2y = 4

2y = 4

y = 4/2

y = 2

substitute for y in any of the equations:

using equation 1:

x + 4(2) = 8

x + 8 = 8

x = 8-8

x = 0

Since we have two equations and a solutionof x and y (indicating their point of intersection), the system has one solution (option B)