Solve for x, y and z when
12x + 15y + 5z = 158 (1)
4x + 3y + 4z = 50 (2)
5x + 20y + 2z = 148 (3)
Deez Nuts
(x,y,z) = (4,6,4)
To solve for the values of x, y, and z in the given set of linear equations, we can make use of the method of substitution or elimination.
Method 1: Substitution Method
Step 1: Choose any one equation from the given system and solve it for one variable in terms of the other two variables.
Let's solve equation (1) for x:
12x + 15y + 5z = 158
12x = 158 - 15y - 5z
x = (158 - 15y - 5z)/12
Step 2: Substitute the expression obtained for x in step 1 into the remaining two equations and solve for the two variables.
Substituting x into equation (2):
4((158 - 15y - 5z)/12) + 3y + 4z = 50
Now solve for y.
Substituting x into equation (3):
5((158 - 15y - 5z)/12) + 20y + 2z = 148
Now solve for z.
Step 3: Substitute the values of y and z obtained in step 2 back into the expression for x from step 1, and solve for x.
Method 2: Elimination Method
Step 1: Multiply the equations by suitable constants so that when added or subtracted, one of the variables will be eliminated.
You can choose to eliminate any variable by multiplying the equations by different constants.
Step 2: Add or subtract the equations obtained in step 1 to eliminate one variable.
By adding or subtracting the equations, you can eliminate one variable and get a new equation.
Step 3: Solve the new equation obtained in step 2 for one variable.
Step 4: Substitute the value of the variable found in step 3 into one of the original equations, and solve for another variable.
Step 5: Substitute the values of two variables found in steps 3 and 4 into any of the original equations to solve for the remaining variable.
Following one of these methods, you can find the values of x, y, and z in the given system of linear equations.