How do you solve the simultaneous equations #x(y-1)=3# and #y=x-1#?

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Answer 1 · 2015-08-03T01:53:44

#color(red)(x=3,y=2)# and #color(red)(x=-1,y=-2)#

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] #x(y-1)=3#
[2] #y=x-1#

Step 2. Solve for one variable in terms of the other.

[2] #y=x-1#

Since this is already done for us, we can go on to the next step.

Step 3. Substitute Equation 2 in Equation 1 and solve for #x#.

#x(y-1)=3#

#x(x-1-1)=3#

#x(x-2)=3#

#x^2-2x=3#

#x^2-2x-3=0#

#(x-3)(x+1)=0#

#x-3=0# and #x+1=0#

#x=3# and #x=-1#

Step 4. Substitute each value of #x# in Equation 2

If #x=3#,
#y=3-1#
#y=2#

If #x=-1#,
#y=-1-1#
#y=-2#

Solutions: #x=3,y=2# and #x=-1,y=-2#

Check: Substitute the values of #x# and #y# in Equations 1 and 2.

Check No. 1: (#3,2#)

#3(2-1)=3#
#3(1) =3#
#3=3#

#2=3-1#
#2=2#

It checks!

Check No. 2: (#-1,-2#)

#-1(-2-1)=3#
#-1(-3)=3#
#3=3#

#-2=-1-1#
#-2=-2#

It checks!

Our solutions are correct.