Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to solve linear-quadratic systems of equations.

Q1:

Find all of the solutions to the simultaneous equations π¦ + π₯ = 7 and 2 π₯ + π₯ + 3 π¦ = 2 1 2 .

Q2:

Find the set of points of intersection of the graphs of π₯ + 5 π¦ = 0 and π¦ = β π₯ 2 .

Q3:

Given that π₯ + π₯ π¦ = 1 8 2 , and π₯ + π¦ = 6 , find the value of π₯ .

Q4:

Find the set of points of intersection of the graphs of π₯ + π¦ = 8 and π₯ + π¦ = 5 0 2 2 .

Q5:

Find all of the solutions to the simultaneous equations π¦ + 2 π₯ = 3 and π₯ + π₯ π¦ + π¦ = 3 2 2 .

Q6:

Find all of the solutions to the simultaneous equations π₯ β π¦ = 2 6 and π₯ π¦ = 1 2 0 .

Q7:

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

Q8:

Find all of the solutions to the simultaneous equations π₯ β π¦ = 6 and π₯ β 9 π₯ π¦ + π¦ = 3 6 2 2 .

Q9:

Find the set of points of intersection of the graphs of π₯ β π¦ = 0 and 6 π₯ β π¦ = 4 5 2 2 .

Q10:

Find the set of points of intersection of the graphs of π₯ = β 6 + π¦ and π₯ β π¦ = 2 4 2 2 .

Q11:

Find the set of points of intersection of the graphs of π₯ + π¦ + 6 = 5 and π₯ β π¦ = 3 5 2 2 .

Q12:

Find the set of points of intersection of the graphs of π₯ β π¦ = β 7 and π₯ + π¦ β 2 π₯ π¦ + 5 π¦ = 1 4 2 2 .

Q13:

Find the set of points of intersection of the graphs of π₯ + 1 0 π¦ = 5 and 1 0 0 π¦ β π₯ = 7 5 2 2 .

Q14:

Given that π¦ = 4 β π₯ and ( π₯ + π¦ ) + π¦ = 1 2 , find π¦ .

Q15:

Solve the given simultaneous equations.

Q16:

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

Q17:

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

Q18:

A fatherβs age is 10 more than 2 times his sonβs age. The sum of the squares of their ages is 4 more than 3 times the product of their ages. What are their ages?

Q19:

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

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.

Q21:

What is the π₯ -coordinate of the point where the line 2 π₯ + π¦ = β 1 1 meets the curve π¦ = 4 π₯ + 4 π₯ β 3 2 ?

Q22:

Find the two points on the line 1 8 π₯ β π¦ = 1 2 with a π¦ -coordinate which is six times the square of the π₯ coordinate.

Q23:

Solve the simultaneous equations

Q24:

Given that ( π + 6 , β 4 ) = οΉ π , β 4 π ο 2 , determine the values of π and π .

Q25:

Given that π π = 6 and π π = 2 4 2 , determine the value of π .

Donβt have an account? Sign Up