Exercise 1 Page 165

The given system consists of equations of planes. Let's use the Elimination Method to find a solution to this system. Notice that in the third equation, there is no b-term. -3a-4b+2c=28 & (I) a+3b-4c=-31 & (II) 2a+3c=11 & (III) We can start with creating additive inverse coefficients for b in the first and second equations. Then we can add or subtract these equations to eliminate b from the second equation.

Next, we use our two equations that only contains a and c to solve for the value of one of the variables. We will once again apply the Elimination Method, but this time will be similar to when using it in a system with only two variables.

Now that we know that c=5, we can substitute it into the second equation to find the value of a.

The value of a is -2. Let's substitute both values into the first equation to find b.

The solution to the system is (-2,-3,5). This is the singular point at which all three planes intersect.