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Start with the equation z = 1, then do any valid manipulation on the left side, and the same manipulation on the right side. The manipulations that won't change the solution set are: adding the same constant to both side; multiplying both sides by the same non-zero constant. Squaring and taking roots will sometimes add additional solutions, or eliminate solutions.
For example, and this is just an example of what you can do:
z = 1
Multiply both sides by 2:
2z = 2
Add 5 to both sides:
2z + 5 = 7
Add 1 to each side:
2z + 6 = 8
Multiply both sides by 2:
4z + 12 = 16
Add z to both sides:
5z + 12 = z + 16
Add your answer:
Earn +20 pts
What is the ordered triple of x plus y plus z equals 12 and y equals 1 and x-y-z equals 0?
x + y + z = 12 y = 1 x - y - z = 0 Substitute y = 1 in the other two equations: x + 1 + z = 12 so that x + z = 11 and x - 1 - z = 0 so that x - z = 1 Add these two equations: 2x + 0z = 12 which implies that x = 6 and then x + z = 11 gives z = 5 So the solution is (x, y, z) = (6, 1, 5)
X varies directly with y and inversely with z x equals 0.12 when y equals 12 and z equals 2 Find x when y equals 1200 and z equals 1?
x = 24
How do you prove that xyz equals 1 if x equals logy z and y equals logz x and z equals logx y?
If xyz=1, then it is very likely that x=1, y=1, and z=1. So plug these in. 1=logbase1of1, 1=logbase1of1, 1=logbase1of1. You end up with 1=1, 1=1, and 1=1. That's your proof.
X varies directly with y and inversely with z x equals 0.25 y equals 10 and z equals 20 find x when y is 20 and z is 10?
1
If 4z-1 equals 9 what is z?
4z - 1 = 9 4z = 10 (add 1 to both sides) z = 2.5 (divide both sides by 4)
What is the ordered triple of x plus y plus z equals 12 and y equals 1 and x-y-z equals 0?
x + y + z = 12 y = 1 x - y - z = 0 Substitute y = 1 in the other two equations: x + 1 + z = 12 so that x + z = 11 and x - 1 - z = 0 so that x - z = 1 Add these two equations: 2x + 0z = 12 which implies that x = 6 and then x + z = 11 gives z = 5 So the solution is (x, y, z) = (6, 1, 5)
Solve the following system of equations What is the value of y when x - y - z equals 0 3x plus y - z equals 2 x plus 2y plus z equals 0?
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
What is th ordered triple of these equations x - 2y plus 3z equals -3 2x - 3y - z equals 7 3x plus y - 2z equals 6?
The ordered triple is (x, y, z) = (1, -1, -2)
Which classifaction best describes the following system of equations x-y-z equals 0 2x-y plus 2z equals 1 x-y plus z equals -2 is it consistent incosistnet dependent or independent?
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
Find the solution to the system of equations 3x plus y plus z equals 6 3x - y plus 2z equals 9 y plus z equals 3?
3x + y + z = 63x - y + 2z = 9y + z = 3y + z = 3y = 3 - z (substitute 3 - z for y into the first equation of the system)3x + y + z = 63x + (3 - z) + z = 63x + 3 = 63x = 3x = 1 (substitute 3 - z for y and 1 for x into the second equation of the system)3x - y + 2z = 93(1) - (3 - z) + 2z = 93 - 3 + z + 2z = 93z = 9z = 3 (which yields y = 0)y = 3 - z = 3 - 3 = 0So that solution of the system of the equations is x = 1, y = 0, and z = 3.
How do you solve for equations x-y-z equals 1 2x plus y-z equals 1 x-y plus 2z equals 7?
(1) x - y - z = 1(2) 2x + y - z = 1(3) x - y + 2z = 7With linear equations involving three unknowns use different pairs of equations to eliminate the same unknown. This will result in two (or perhaps three if needed) equations containing two unknowns.For this exercise, eliminate z as the first step.Subtract equation (1) from equation (2)2x + y - z - (x - y - z) = 1 - 1 : (4) x + 2y = 0Multiply equation (2) by 2 then add to equation (3)4x + 2y - 2z + x - y + 2z = 2 + 7 : (5) 5x + y = 9Multiply equation (5) by 2 then subtract equation (4)10x + 2y - (x + 2y) = 18 - 0 : 9x = 18 : x = 2Substituting for x in equation (5) gives 10 + y = 9 : y = -1Substituting for x and y in equation (2) gives 4 -1 -z = 1 : z = 2
What are some examples of conformal math equations?
Conformal mapping equations in the field of mathematics take the form of w=f(z), meaning w is a function of z. An analytic function conforms to any point where the derivative of the function is non-zero. Examples of equations include f(z)=1/z or f(z)=(z^2)/1 but in actuality there are an infinite number of potential equations and transformations in conformal mapping.
What are the solutions to the simultaneous equations of x -y -z equals 0 and 2x -y plus 2z equals 1 and x -y plus z equals -2?
1st equation: x-y-z = 0 2nd equation: 2x-y+2z = 1 3rd equation: x-y+z = -2 Multiply all terms in 1st equation by 3 then add all equations together:- So: 6x-5y = -1 Multiply all terms in 3rd equation by 2 and subtract it from the 2nd equation:- So: y = 5 Therefore by means of substitution: x = 4, y = 5 and z = -1
What are 3 real rational solutions to this system of equations z equals x squared y equals z squared x equals y squared?
The two rational solutions are (0,0,0) and (1,1,1). There are no other real solutions.
Solve this system of equations 5x plus 3y plus z equals -29 x-3y plus 2z equals 23 14x-2y plus 3z equals -18?
Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.
Find the area below the normal curve z equals -2 and z equals 1?
0.8185
If y times x-1 equals z then x equals?
y * (x-1) = z Express as x,divide both sides by y(x - 1) = z/yadd 1 on both sidesx = z/y + 1
