Question

Find the complete solution of the system 5x+3y+11z=37 3y+z=12 5x+9y+13z=61

Answer 1

Answer:

$y = \displaystyle\frac{12-z}{3}\\\\x = -2z + 5$

Step-by-step explanation:

We are given a system of equation:

$5x+3y+11z=37\\3y+z=12\\5x+9y+13z=61$

To find a solution to the given system, we follow the given steps.

1. Subtracting second equation from first and third equation, we get:

$5x+3y+11z-3y-z=37-12\\5x+10z = 25\\5x+9y+13z-3(3y+z) = 61 - 36\\5x + 10z = 25$

2. After eliminating z to obtain two equations in two variable, we observe that the two equations obtained were same.

So we have three equations that will all graph in the same plane.

Thus, there are infinite number of solution to the given system of equation.

We can write the values of x and y in the form of z:

$y = \displaystyle\frac{12-z}{3}\\\\5x + 12 - z + 11z = 37\\5x = -10z + 25\\x = -2z + 5$