How do you solve the system x= 175+15y, .196x= 10.4y, z=10*y?

1 Answer
Oct 18, 2016

x=53.05
y=-8.13
z=-81.3

Explanation:

To begin, plug in a equation for a variable that is already isolated. There are two variables that are already isolated, and those are x and z. You could choose either to work with, doesn't matter, but I'm going to use x

So, plug the equation for x into another equation that has that same variable in it. Which would be:

.196x=10.4y

To begin, plug x equation into .196x=10.4y

.196(175+15y)=10.4y

Distribute .196 throughout the set of parenthesis

34.3+2.94y=10.4y

Begin to isolate y by subtracting 34.3 on both sides of the equation

2.94y=-23.9

Isolate y by dividing 2.94 on both sides of the equation

y=-8.13

Now, we have solved for one of the variables. The next thing to do is plug y into another equation that contains y in it. An easy one to use would be x=175+15y because x is already isolated

So, plug y=-8.13 into x=175+15y

x=175+15(-8.13)

Distribute 15 throughout the set of parenthesis

x=175-121.95

Subtract

x=53.05

And now we have solved for y and x. The only variable left is z

To solve for z, you have to plug y=-8.13 into the equation

z=10(-8.13)

Multiply

z=-81.3

x=53.05
y=-8.13
z=-81.3