Question

Two equations are given below:

a − 3b = 4
a = b − 2

What is the solution to the set of equations in the form (a, b)?

(−2, −2)
(−3, −1)
(−9, −7)
(−5, −3)

Answer 1

Since the second equation gives a value for a, we can substitute it into the other equation to find a value for B.

Let's substitute b-2 into the first equation wherever there is an a.

a - 3b = 4
(b-2) - 3b = 4
b - 2 - 3b = 4
-2 - 2b = 4
-2b = 6
b = -3

Now let's find a by substituting -3 into either of the equations to find the value of a.

a = b - 2
a = -3 - 2
a = -5

So your solution set  is (-5, -3)

Answer 2

The solution to the set of equations in the form (a, b) is (-5, -3).

Hence, 4th option is the right choice.

What are simultaneous equations?

A system of equations, also known as an equation system or a set of simultaneous equations, is a finite collection of equations for which common solutions are found.

How do we solve the given question?

We are given two equations in a and b and are asked to find the solution to them. The equations are:

a - 3b = 4 . . . . . . . . . . . . . . (1)

a = b - 2 . . . . . . . . . . . . . . (2)

We substitute the value of a = b - 2 from (2) in (1) to get,

(b - 2) -3b = 4

or, b - 2 - 3b = 4.

or, b -2 - 3b + 2 = 4 + 2 (adding 2 two both sides of the equation)

or, -2b = 6 (simplifying)

or, -2b/(-2) = 6/(-2) (dividing both sides by -2)

or, b = -3 (simplifying)

Now, we substitute this value of b = -3, in (2) to get

a = (-3) - 2

or, a = -5.

∴ (a, b) = (-5, -3)

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