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

Question

Ethan Adkins · Accepted Answer

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

Using the method of elimination is one approach.

First, input the equations.

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

Step 2: Calculate one variable using the other as a reference.

[2] #y=x-1#

We're done with this, so let's move 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 verifies!

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

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

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

It verifies!

Our answers are accurate.

Kennedy Adams · Answer

undefined To solve the simultaneous equations x(y-1)=3 and y=x-1, you can substitute the expression for y from the second equation into the first equation. Then solve for x, and use that value of x to find the corresponding value of y.