What are the intercepts of -4x 6y-5z=60

X intercept is when y and z=0
yinter cept is when x and z =0
zintercept is when x and y =0

set to zero and solve

xint
-4x+6(0)-5(0)=60
-4x=60
divide -4
x=-15
xint is (-15,0,0)

ying
-4(0)+6y-5(0)=60
6y=60
divide by 6
y=10
yint is (0,10,0)

zint
-4(0)+6(0)-5z=60
-5z=60
divide by -5
z=-12
zint is (0,0,-12)

xint is (-15,0,0)
yint is (0,10,0)
zint is (0,0,-12)

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.