Question

In the system of linear equations below, q and r are constants. The solutions to the system is (-1,4). What are the values of q and r?

Answer 1

To find the values of q and r, we need to solve the system of linear equations using the given solution (-1,4). The values of q and r are q = 0 and r = 1.

Step-by-step explanation:

To find the values of q and r, we need to solve the system of linear equations using the given solution (-1,4).

Let's substitute the values of x and y into the equations:

Equation 1: q - r = -1

Equation 2: 4q + r = 4

We can solve these equations using different methods like substitution, elimination, or matrices. Let's use the elimination method to solve this system.

We multiply Equation 1 by 4 and Equation 2 by 1 to eliminate the r variable:

Multiplying Equation 1 by 4: 4q - 4r = -4

Multiplying Equation 2 by 1: 4q + r = 4

Adding these two equations together, we get:

8q = 0

Dividing both sides by 8, we find that q = 0.

Substituting q = 0 into Equation 1, we can solve for r:

0 - r = -1

Subtracting -r from both sides, we get r = 1.

Therefore, the values of q and r are q = 0 and r = 1.