# Show that each of the following systems of equations has a unique solution and solve it: , x - 2y = 2.

Given: 2x + 3y = 18 – eq 1

x - 2y = 2 – eq 2

Here,

a1 = 2, b1 = 3, c1 = 18

a2 = 1, b2 = - 2, c2 = 2 = , = Here,  Given system of equations have unique solutions.

Now,

In – eq 1

2x = 18 – 3y

X = Substitute x in – eq 2

we get, – 2y = 2 = 2

18 – 3y – 4y = 4

18 – 7y = 4

7y = 18 – 4

7y = 14

y = = 2

y = 2

Now, substitute y in – eq 1

We get,

x – 2×(2) = 2

x – 4 = 2

x = 2 + 4

x = 6

x = 6

x = 6 and y = 2

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