Question

Consider the linear system of equations. y = –x + 9 y = 0.5x – 6 If the solution is (a,–1), what is a? a =

Answer 1

The value of a is 10.

Explanation:

We are given with the following pair of the linear system of equations below;

`y = -x+9` and
`y = 0.5x-6`.

Also, the solution is given as (a, -1).

To find the value of 'a', we have to substitute the solution in the equation because it is stated that (a, -1) is the solution of the given two equations.

So, the x coordinate value of the solution is a and the y coordinate value of the solution is (-1).

First, taking the equation;

`y = -x+9`

Put the value of x = a and y = -1;

(-1) = -(a) + 9

a = 9 + 1 = 10

Now, taking the second equation;

`y = 0.5x-6`

Put the value of x = a and y = -1;

`(-1) = 0.5(a)-6`

0.5a = 6 - 1

0.5a = 5

`a=(5)/(0.5)`

a = 10

Since we get the value of a = 10 from the equations, so the value of a is 10.