# Worksheet: Linear-Quadratic Systems of Equations

In this worksheet, we will practice solving linear-quadratic systems of equations.

**Q3: **

Given that , and , find the value of .

**Q6: **

Find all of the solutions to the simultaneous equations and .

- A
- B
- C
- D
- E

**Q7: **

Solve the simultaneous equations giving your answers to two decimal places.

- A and , and
- B and , and
- C and , and
- D and , and
- E and , and

**Q9: **

Find the set of points of intersection of the graphs of and .

- A
- B
- C
- D

**Q10: **

Find the set of points of intersection of the graphs of and .

- A
- B
- C
- D

**Q11: **

Find the set of points of intersection of the graphs of and .

- A
- B
- C
- D

**Q12: **

Find the set of points of intersection of the graphs of and .

- A
- B
- C
- D

**Q13: **

Find the set of points of intersection of the graphs of and .

- A
- B
- C
- D

**Q14: **

Given that and , find .

**Q15: **

Solve the given simultaneous equations.

- A and , and
- B and , and
- C and , and
- D and , and
- E and , and

**Q16: **

The sum of two numbers is 11 and the sum of their squares is 65. What are the numbers?

- A ,
- B ,
- C ,
- D ,

**Q17: **

Two numbers have a difference of 6. If the sum of their squares is 68, what are the numbers?

- A or
- B or
- C or
- D or

**Q18: **

A father’s age is 10 more than 2 times his son’s age. The sum of the squares of their ages is 4 more than 3 times the product of their ages. What are their ages?

- A the father’s age , the son’s age
- B the father’s age , the son’s age
- C the father’s age , the son’s age
- D the father’s age , the son’s age
- E the father’s age , the son’s age

**Q20: **

The difference between the perimeters of two square
gardens is 4 m and the difference between their areas is 39 m^{2}.
Find the side length of each garden.

- A80 metres, 76 metres
- B21 metres, 18 metres
- C84 metres, 72 metres
- D20 metres, 19 metres

**Q21: **

What is the -coordinate of the point where the line meets the curve ?

- A
- B
- C
- D

**Q22: **

Find the two points on the line with a -coordinate which is six times the square of the coordinate.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q23: **

Solve the simultaneous equations

- A and , and
- B and , and
- C and , and
- D and , and
- E and , and

**Q24: **

Given that , determine the values of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q25: **

Given that and , determine the value of .

- A
- B
- C
- D
- E