How do you solve the following system?: #-2x -5y =17, 3x -y = -61#

Question

Ethan Adkins · Accepted Answer

The joint values that satisfy both equations are:

#(x,y)->(-322/17,71/17)#

These are equations of straight line graphs. The gradients are different which means that at some point they will cross.

At that instance they will both share the same values for #x# and #y#. It is what you are determining when solving such a system

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given

#-2x-5y=17" "#.................................(1)
#3x-y=-61" "#.................................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the value of "x)#

Write equation (2) as :

#y=3x+61" "................................(2_a)#

Using #(2_a)# substitute for #y# in equation (1)
so that we have only 1 unknown variable

#-2x-5(3x+61)=17#

Multiply out the brackets

#-2x-15x-305=17#

add 305 to both sides

#-17x=322#

Multiply both sides by (-1)

#+17x=-322#

#color(blue)(x=-322/17)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the value of "y)#

Substitute for #x# in equation (1)

#-2(-322/17)-5y=17#

#644/17-17=5y#

#color(blue)(y=355/17xx1/5=71/17)#

Kennedy Adams · Answer

undefined To solve the system, you can use either the substitution method or the elimination method.