How to solve the equation:
36x-15y+50z=-10
2x+25y=40
54x-5y+30z=-160
How to solv -x+5y=19
X+2y=16
To solve this system of equations, we will use a method called "elimination" or "substitution" to find the values of x, y, and z.
Let's start by using the elimination method to eliminate the variable x.
Multiply equation 2 by 18, equation 1 by 1, and equation 3 by 3 to make the coefficients of x in equations 1 and 3 the same as the coefficient of x in equation 2.
Equation 1: 36x - 15y + 50z = -10
Equation 2: 36x - 450y = 720
Equation 3: 162x - 15y + 90z = -480
Now, subtract equation 2 from equation 1 and equation 2 from equation 3:
(Equation 1) - (Equation 2): 36x - 15y + 50z - (36x - 450y) = -10 - 720
(Equation 3) - (Equation 2): 162x - 15y + 90z - (36x - 450y) = -480 - 720
Simplifying the above equations, we get:
Equation 4: 435y + 50z = 710
Equation 5: 126x - 435y + 90z = -1200
Now, let's use the elimination method again to eliminate the variable y.
Multiply equation 4 by 126 and equation 5 by 435 to make the coefficients of y in both equations the same.
Equation 4: 54690y + 6300z = 89760
Equation 5: 54690y + 19575z = -522000
Subtract equation 4 from equation 5:
(Equation 5) - (Equation 4): 54690y + 19575z - (54690y + 6300z) = -522000 - 89760
Simplifying the above equation, we get:
Equation 6: 13275z = -611760
Lastly, divide both sides of equation 6 by 13275 to solve for z:
z = -611760 / 13275
Now that we have the value of z, we can substitute it back into one of the original equations to solve for x and y. Let's substitute it into equation 1:
36x - 15y + 50 (-611760 / 13275) = -10
Solve for x and y using this equation.