Question

Solve the system of equations.

5x – y = 5
5x2 – y = 5

Answers:
(0, 5) and (0, –5)
(1, 0) and (0, –5)
(2, 5) and (1, 0)
(3, 10) and (2, 15)

Answer 1

Option 2: (1, 0) and (0, -5)

Explanation:

Let's solve this system of equations using the elimination method.

Start by labelling the two equations.

5x -y= 5 -----(1)

5x² -y= 5 -----(2)

(2) -(1):

5x² -y -(5x -y)= 5 -5

Expand:

5x² -y -5x +y= 0

5x² -5x= 0

Factorise:

5x(x -1)= 0

5x= 0 or x -1= 0

x= 0 or x= 1

Now that we have found the x values, we can substitute them into either equations to solve for y.

Substitute into (1):

5(0) -y= 5 or 5(1) -y= 5

0 -y= 5 or -y= 5 -5

y= -5 or -y= 0

y= 0

Thus, the solutions are (0, -5) and (1, 0).