Add
3x + 2y - z = 7
-3x + y - 2z = -14
to eliminate
To eliminate the variable "x" from the system of equations:
Step 1: Multiply the first equation by -1.
-1(3x + 2y - z) = -1(7)
-3x - 2y + z = -7
Step 2: Add the two equations together.
(-3x + y - 2z) + (-3x - 2y + z) = -14 + (-7)
-6x - y - z = -21
The eliminated equation is -6x - y - z = -21.
Can you subtract the equations?
Apologies for the mistake. Yes, we can subtract the equations to eliminate "x".
The given equations are:
3x + 2y - z = 7 ...(Equation 1)
-3x + y - 2z = -14 ...(Equation 2)
To eliminate "x", we can subtract Equation 2 from Equation 1.
(Equation 1) - (Equation 2) gives:
3x - (-3x) + 2y - y - z - (-2z) = 7 - (-14)
This simplifies to:
6x + y + z = 21
So, subtracting the equations, we get the equation 6x + y + z = 21.
To eliminate one variable and solve the system of equations, you can use the method of elimination. Follow the steps below:
1. Multiply one or both equations by a constant to create coefficients for one variable that will cancel out when the equations are added or subtracted.
We will multiply the first equation by 3 and the second equation by -1 to create oppositely signed coefficients for the x variable:
3(3x + 2y - z) = 3(7) -> 9x + 6y - 3z = 21
-1(-3x + y - 2z) = -1(-14) -> 3x - y + 2z = 14
2. Add or subtract the equations to eliminate one variable.
(9x + 6y - 3z) + (3x - y + 2z) = 21 + 14
Combine like terms: 9x + 3x + 6y - y - 3z + 2z = 35
Simplify: 12x + 5y - z = 35
The equation 12x + 5y - z = 35 is the result of adding the given equations.
To eliminate variables and solve for the system of equations:
Step 1: Multiply one or both of the equations by constant(s) so that the coefficients of one of the variables will be equal (but with opposite signs) in both equations. In this case, we need to eliminate the x variable. Let's multiply the first equation by 3 and the second equation by -1.
3(3x + 2y - z) = 3(7) --> 9x + 6y - 3z = 21
-1(-3x + y - 2z) = -1(-14) --> 3x - y + 2z = 14
The new system of equations is:
9x + 6y - 3z = 21
3x - y + 2z = 14
Step 2: Now, add the two equations together, and eliminate the x variable:
(9x + 6y - 3z) + (3x - y + 2z) = 21 + 14
Combining the like terms:
12x + 5y - z = 35
The result is the equation after eliminating the x variable.
Therefore, the equation obtained after eliminating the variables in the given system of equations is:
12x + 5y - z = 35.