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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:

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

Q4:

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

Q5:

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.

Q6:

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?

Q7:

Solve the simultaneous equations

Q8:

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

Q9:

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

Q10:

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

Q11:

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

Q12:

Find all of the solutions to the simultaneous equations π₯ + π¦ = 4 2 and π₯ β π₯ π¦ = 0 2 .

Q13:

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

Q14:

Find all of the solutions to the simultaneous equations π₯ β π¦ = 7 and π₯ β 3 π₯ π¦ + π¦ = 4 9 2 2 .

Q15:

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

Q16:

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

Q17:

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

Q18:

Solve the given simultaneous equations.

Q19:

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 .

Q20:

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 .

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

Q23:

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

Q24:

Find the set of points of intersection of the graphs of π₯ = 6 β π¦ and π₯ β π¦ = 1 4 4 2 2 .

Q25:

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

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