Find the coordinates of the points A and B where the line 5x+y=10 cuts x-axis and y-axis respectively?

The line cuts the x-axis and y-axis at the x-intercept and the y-intercept.

X-intercept: value of #x# when #y=0#

Substitute #0# for #y#, and solve for #x#.

#5x+0=10#

#5x=10#

Divide both sides by #5#.

#x=10/5#

#x=2#

Point A: #(2,0)# #larr# x-intercept

Y-intercept: value of #y# when #x=0#

Substitute #0# for #x#.

#5(0)+y=10#

Simplify.

#0+y=10#

#y=10#

Point B: #(0,10)# #larr# y-intercept

graph{5x+y=10 [-14.24, 14.23, -7.12, 7.12]}

#5x+y=10# is the equation of a straight line.
When you want to find the intersection of a straight line with the axis you basically want to know what is the value of #y# when #x# is equal to #0# (y-axis intercection) and what is the value of #x# when #y# is equal to #0# (x-axis intecection).
x-axis:
when #y=0# the equation becomes:
#5x+0=10=>x=10/5=>x=2#
so the first point is #A=(2,0)#

y-axis:
when #x=0# the equation becomes:
#0+y=10=>y=10#
so the second point is #B=(0,10)#
graph{5x+y=10 [-10, 10, -5, 5]}

#"to find where the line crosses the x and y axes"#

#• " let x = 0, in the equation for y-intercept"#

#• " let y = 0, in the equation for x-intercept"#

#x=0rArr0+y=10rArry=10larrcolor(red)"y-intercept"#

#y=0rArr5x+0=10rArrx=2larrcolor(red)"x-intercept"#

#"crosses x-axis at "A(2,0)" and y-axis at "B(0,10)#
graph{(y+5x-10)((x-2)^2+(y-0)^2-0.04)((x-0)^2+(y-10)^2-0.04)=0 [-20, 20, -10, 10]}