Solve Using System Of Equations, X - Y = 0, -3x - Y = 2

Solve using System Of Equations
x - y = 0
-3x - y = 2

 

Answer:

The solution (x, y) to the  system is (-1/2, -1/2) where x= -1/2 and y= -1/2.

The graph intersects at point (-1/2, -1/2).

The system has one solution and therefore consistent and independent.

Step-by-step explanation:

Equation (1):

x - y = 0

x = y

Equation (2):

-3x - y = 2

Solve for y by substitution in Equation 2 where x = y:

-3x - y = 2

-3(y) - y = 2

-3y - y = 2

-4y = 2

-4y/-4 = 2/-4

y = -1/2

Subsitute -1/2 to y in Equation (1):

x - y = 0

x - (-1/2) = 0

x + 1/2 = 0

x = -1/2

The solution (x, y) to the  system is (-1/2, -1/2).

The graph intersects at point (-1/2, -1/2).

The system has one solution and therefore consistent and independent.

Check:

Equation (1):

x - y = 0

(-1/2) - (-1/2) = 0

-1/2 + 1/2 = 0

0 = 0  (True)

Equation (2):

-3x - y = 2

-3(-1/2) - (-1/2) = 2

3/2 + 1/2 = 2

4/2 = 2

2 = 2  (True)