How do you solve the system of equations 7x + 5y + 7z = 60, 15x + 2z = - 195, and 5z = 75?

2 Answers
Aug 6, 2018

x=-15
y=12
z=15

Explanation:

First solve for z using the third equation

z=75/5=15

Now that we know z, we can plug it into the second equation and solve for x

15x+2(15)=-195

15x=-225

x=-15

Now we can find y using the values of x and z and plugging them into the first equation

7(-15)+5y+7(15)=60

5y=60

y=12

Aug 6, 2018

x =-15
y = 12
z=15

Explanation:

This question is far easier than it appears at first.

The key idea is that if a a linear equation has 1 variable, there will be one solution, but as soon as there are 2 variable, 2 equations are required and likewise for 3 variables, there must be 3 equations.

We have all of these scenarios presented here.

Solve the 3rd equation first as it only has 1 variable,

5z = 75
color(blue)(z =15)" "larr now use this value for z in the 2nd equation:

15x +2color(blue)(z) = -195
15x +2color(blue)((15)) = -195
15x +color(blue)(30) = -195
15x = -225
color(green)(x =-15)" "larr use this value for x in the first equation

7color(green)(x)+5y+7color(blue)(z)=60
7color(green)((-15))+5y+7color(blue)((15))=60

-105 +5y +105 = 60
5y=60
y=12