Let's solve the system of equations step by step:
Simplify the first equation:2(x + y) - x - 6 = 02x + 2y - x - 6 = 0x + 2y - 6 = 0x = 6 - 2y
Substitute the value of x into the second equation:3x - (x - y) = 03(6 - 2y) - (6 - 2y - y) = 018 - 6y - 6 + 2y = 012 - 4y = 04y = 12y = 3
Substitute the value of y back into the first equation:x = 6 - 2(3)x = 6 - 6x = 0
Check the values in the third equation:(x + 5y = -2.5)(0 + 5(3)) = -2.50 + 15 = -2.515 = -2.5 (not true)
Therefore, the system of equations is inconsistent and does not have a solution.
Let's solve the system of equations step by step:
Simplify the first equation:
2(x + y) - x - 6 = 0
2x + 2y - x - 6 = 0
x + 2y - 6 = 0
x = 6 - 2y
Substitute the value of x into the second equation:
3x - (x - y) = 0
3(6 - 2y) - (6 - 2y - y) = 0
18 - 6y - 6 + 2y = 0
12 - 4y = 0
4y = 12
y = 3
Substitute the value of y back into the first equation:
x = 6 - 2(3)
x = 6 - 6
x = 0
Check the values in the third equation:
(x + 5y = -2.5)
(0 + 5(3)) = -2.5
0 + 15 = -2.5
15 = -2.5 (not true)
Therefore, the system of equations is inconsistent and does not have a solution.