Question

What is the solution to the following system of equations?

(3,6), (4,1), (1,4), (3,−4)

a) No solution
b) x=2,y=3
c) x=1,y=2
d) x=3,y=−2

Answer 1

The solution to the given system of equations is x = 1.29, y = -0.14.

Step-by-step explanation:

The given system of equations can be written as:

3x + 6y = 3

4x + y = 1

x + 4y = -4

3x - 4y = 0

To find the solution, we can solve this system using elimination or substitution:

Using elimination, we can add the first equation and the third equation, and the second equation and the fourth equation, to eliminate x:

7y = -1

-3y = -3

From these equations, we can solve for y:

y = -1/7

Substituting this value of y into any one of the equations, we find:

3x + 6(-1/7) = 3

3x - 6/7 = 3

3x = 21/7 + 6/7

3x = 27/7

x = 27/7 * 1/3

x = 9/7

Therefore, the solution to the system of equations is x = 9/7, y = -1/7, which can be written as x = 1.29, y = -0.14 (rounded to two decimal places).