What are x and y if #5x - 2y = -5# and #y - 5x = 3#?
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"What does Hess's law say about the enthalpy of a reaction?"
#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#
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]}
