Question

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

−2x + 5y = 7

2x + 9y = 7 and (−1, 1)

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:

-2x + 5y = 7 …… (1)

2x + 9y = 7 …… (2)

 

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

 

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

-2(-1) + 5(1) = 7

           2 + 5 = 7

                 7 = 7

 

Thus, (-1, 1) satisfies (1).

 

Now, substitute x = -1 and y = 1 in (2) as shown below:

2(-1) + 9(1) = 7

         -2 + 9 = 7

                7 = 7

 

Thus, (-1, 1) satisfies (2).

 

Therefore, given ordered pair (-1, 1) is a solution of given system of linear equations.

Therefore, given ordered pair (-1, 1) is a solution of given system of linear equations.