Algebra 9

4 marks · Hard

Solve the simultaneous equations:

(a)

Write down the equation to solve for \( x \ ).

[1 mark]

(b)

Solve the equation to find all possible values of \( x \ ). Give your answers to 2 decimal places.

[2 marks]

(c)

For each value of \( x \ ), find the corresponding value of \( y \ ). Give answers to 2 decimal places.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) x^2 - 11x = 0 · must show Subtract linear from quadratic

(b) x = 0.00, x = 11.00 · must show Both x values, rounded as required

Must show: Correct equation for x, Both x values correct to 2dp, Both y values correct to 2dp

Common mistakes: Wrong sign when moving terms; Incorrect use of quadratic formula; Rounding mistakes

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Sets and gets all terms on one side.

M2 (b) · 1 mark · Uses correct method to solve the quadratic . (follow-through)

A1 (b) · 1 mark · Finds both values of (0 and 11, correct to 2dp). (follow-through)

A2 (c) · 1 mark · Finds corresponding values of for both values, correctly rounded. (follow-through)

Worked solution

Set equal to :

Move all terms to one side:

Factorise or use quadratic formula:

So or .

Substitute into either equation (easiest: ):

Substitute :