Question

For the following exercises, determine whether the given ordered pair is a solution to the system of equations.

x + 8y = 43

3x − 2y = −1 and (3, 5)

Answer 1

Consider the system of linear equations in two variables as

a1x + b1y = c1

a2x + b2y = c2

 

The solution of such system of linear equations in two variables is any ordered pair that satisfies each equation independently.

 

Consider system of equations as:

x + 8y = 43 …… (1)

3x – 2y = -1 …… (2)

 

Verify if ordered pair (3, 5) is solution of (1) and (2).

 

Substitute x = 3 and y = 5 in (1) and proceed as following:

(3) + 8(5) = 43

    3 + 40 = 43

          43 = 43

 

Thus, (3, 5) satisfies (1).

 

Now, substitute x = 3 and y = 5 in (2) as shown below:

3(3) – 2(5) = -1

       9 – 10 = -1

              -1 = -1

 

Thus, (3, 5) satisfies (2).

 

Therefore, given ordered pair (3, 5) is a solution of given system of linear equations.

Therefore, given ordered pair (3, 5) is a solution of given system of linear equations.