The solution is (x, y, z) = (2.5, 1, 2.5).
12
6
2x - y = 2 2x - y = -2 This system is inconsistent -- that is, there is no solution. To help see why, let Z = 2x - y and notice Z can't be 2 and -2 at the same time.
3x + 4y - 5z and -2x - 5y + 4z Added together, give (3-2)x + (4-5)y + (-5+4)z = x - y - z
3x + 2 = 82
The solution is (x, y, z) = (2.5, 1, 2.5).
5x-2y+3z-2x-y-4z=3x-3y-z
x, y and z are the variables.
12
6
1st equation: x-y-z = 0 2nd equation: 2x-y+2z = 1 3rd equation: x-y+z = -2 They appear to be simultaneous equations dependent on each other for the solutions which are: x = 4, y = 5 and z = -1
2x - y = 2 2x - y = -2 This system is inconsistent -- that is, there is no solution. To help see why, let Z = 2x - y and notice Z can't be 2 and -2 at the same time.
3x + 4y - 5z and -2x - 5y + 4z Added together, give (3-2)x + (4-5)y + (-5+4)z = x - y - z
x = -1, y = 2, z = -3.x - y - z = 03x + y - z = 2x + 2y + z = 0Adding equation 3 to equations 1 and 2 gives new equations 1 & 2:2x + y = 04x + 3y = 2Doubling the [new] equation 1 and subtracting from the [new] equation 2 gives:y = 2Substituting back into [new] equation 1 gives:2x + 2 = 0 ==> x = -1Substituting back into the original equation 1 gives:-1 - 2 - z = 0 ==> z = -3Check by substituting back into original equations:3x + y - z = 3(-1) + (2) - (-3) = -3 + 2 + 3 = 2x + 2y + z = (-1) + 2(2) + (-3) = -1 + 4 - 3 = 0
Actually, 2x + 3y + z is an expression, because it is a mathematical noun.
x + y + z = x + z + y is the commutative property of addition.