What are x and y if #5x - 2y = -5# and #y - 5x = 3#?

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Answer 1 · 2018-05-09T05:08:33

#color(brown)(x = -1/5, y = 2#

#5 x - 2 y = -5, " Eqn (1)"#

#y - 5 x = 3, " Eqn (2)"#

#y = 5x + 3#

Substituting value of y in terms of x in Eqn (1)"#,

#5x - 2*(5x + 3) = -5#

#5x - 10x - 6 = -5#

#-5x = -1, x = -1/5#

#y = 5x + 3 = 5 * (-1/5) + 3 = 2#

Answer 2 · 2018-05-09T06:03:17

The solution is #(-1/5,2)# or #(-0.2,2)#.

We can also use elimination to solve this system of linear equations.

#"Equation 1":# #5x-2y=-5#

#"Equation 2":# #y-5x=3#

Rewrite Equation 2:

#-5x+y=3#

Add: Equation 1 + Equation 2:

#-5x + color(white)(.)y =color(white)(....)3#
#ul(color(white)(..)5x-2y=-5)#
#color(white)(........)-y=-2#

Divide both sides by #-1#. This will reverse the signs.

#y=2#

Substitute #2# for #y# in Equation 2 (either equation will work).

#2-5x=3#

Subtract #2# from both sides.

#-5x=3-2#

#-5x=1#

Divide both sides by #-5#.

#x=-1/5#

The solution is #(-1/5,2)# or #(-0.2,2)#.

graph{(5x-2y+5)(y-5x-3)=0 [-10, 10, -5, 5]}