# Worksheet: Linear-Quadratic Systems of Equations

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

Q1:

Find all of the solutions to the simultaneous equations and .

• A, ; ,
• B, ; ,
• C, ; ,
• D, ; ,

Q2:

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

• A
• B
• C
• D

Q3:

Given that , and , find the value of .

Q4:

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

• A
• B
• C
• D

Q5:

Find all of the solutions to the simultaneous equations and .

• A
• B
• C
• D

Q6:

Find all of the solutions to the simultaneous equations and .

• A
• B
• C
• D
• E

Q7:

• A and , and
• B and , and
• C and , and
• D and , and
• E and , and

Q8:

Find all of the solutions to the simultaneous equations and .

• A
• B
• C
• D

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 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?

• Athe father’s age , the son’s age
• Bthe father’s age , the son’s age
• Cthe father’s age , the son’s age
• Dthe father’s age , the son’s age
• Ethe father’s age , the son’s age

Q19:

A right triangle has a hypotenuse of 35 cm and a perimeter of 84 cm. Find the lengths of the other two sides.

• A21 cm, 26 cm
• B28 cm, 21 cm
• C28 cm, 56 cm
• D56 cm, 42 cm
• E42 cm, 28 cm

Q20:

The difference between the perimeters of two square yards is 4 m and the difference between their areas is 39 m2. Find the side length of each yard.

• A21 metres, 18 metres
• B20 meters, 19 meters
• C84 metres, 72 metres
• D80 metres, 76 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