Question

Solve the following system of equations by the substitution method. x - y = 0 x - y - 2 = 0 What is the solution set? {(1, -1)} {(-1, 1)} Ø

Answer 1

The answer is ∅ ⇒ no solution

Explanation:

* Lets revise how to solve the system of equation by using

substitution method

- At first find a variable in terms of the other one from the

first equation

- Then substitute this value in the second equation

- So you can solve the equation because it has one variable

- After that put the value of the variable in the substitution

equation to find the second variable

* Now lets solve our problem

∵ x - y = 0 ⇒ (1)

∵ x - y - 2 = 0 ⇒ (2)

- Find x in terms of y from 1st equation

∴ x = y

- Substitute this value in the second equation

∴ y - y - 2 = 0

∴ 0 - 2 = 0 ⇒ -2 = 0

* But -2 ≠ 0, that means L.H.S ≠ R.H.S

∴ There is no solution for this system of equations

∴ The answer is ∅