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Simultaneous Equations Involving Squared Terms

In this worksheet, students solve simultaneous equations involving quadratic equations

'Simultaneous Equations Involving Squared Terms' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Solve Simultaneous Equations in 2 Variables

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about finding solutions to more complex simultaneous equations.

 

Example:

x2 + y2 = 2  (eqn 1)
x + y = 2  (eqn 2)


Solve by substituting from the linear equation into quadratic.

From equation 2:    y = 2 - x, so y2 = (2 - x)2 = 4 - 2x + x2

Substituting in equation 1 gives: x2 + 4 - 2x + x2 = 2


2x2 - 4x + 2 = 0
x2 - 2x + 1 = 0
(x - 1)(x - 1) = 0


x = 1 (twice)


In equation 2:    1 + y = 2,   so  y = 1 (twice)

 

Normally, there are two pairs of solutions.

Solve the following simultaneous equations:

x2 + y2 = 8
x + y = 4

x = _______
y = _______

 xy
1
-1
2
-2

Solve the following simultaneous equations:

2x2 + 2y2 = 9
x + y = 3

x = _______
y = _______

 xy
1.5
-1
2.5
-2

Select one solution to these simultaneous equations:

x = 3
y

y = 2x −5

x = _______
y = _______

 xy
1
2
3
4

Select one solution to this pair of simultaneous equations:

x2  = 3y
x + 6 = y

x = _______
y = _______

 xy
3
-1
2
-3

Solve the following simultaneous equations:

25 - 2x2  = 2y2
x  = 5 - y

x = _______
y = _______

 xy
3.5
-1
2.5
-3

Select one solution to this pair of simultaneous equations:

 

xy  = 5
2x - y = 9

x = _______
y = _______

 xy
1
3
5
7

Solve the following simultaneous equations:

18 - y2 = x2
y = 6 - x

x = _______
y = _______

 xy
1
2
3
4

Select one solution to this pair of simultaneous equations:

 

18 - 3y2 = -x
 y = 6 - x

x = _______
y = _______

 xy
1
2
3
4

Select one solution to this pair of simultaneous equations:

 

25 - 2x2 = y- 9
  x = 7 - y

x = _______
y = _______

 xy
1.5
2.5
3
4

Select one solution to this pair of simultaneous equations:

 

x = 3
y

y = 3x − 8 

x = _______
y = _______

 xy
1
2
3
4
  • Question 1

Solve the following simultaneous equations:

x2 + y2 = 8
x + y = 4

x = _______
y = _______

CORRECT ANSWER
 xy
1
-1
2
-2
  • Question 2

Solve the following simultaneous equations:

2x2 + 2y2 = 9
x + y = 3

x = _______
y = _______

CORRECT ANSWER
 xy
1.5
-1
2.5
-2
  • Question 3

Select one solution to these simultaneous equations:

x = 3
y

y = 2x −5

x = _______
y = _______

CORRECT ANSWER
 xy
1
2
3
4
  • Question 4

Select one solution to this pair of simultaneous equations:

x2  = 3y
x + 6 = y

x = _______
y = _______

CORRECT ANSWER
 xy
3
-1
2
-3
  • Question 5

Solve the following simultaneous equations:

25 - 2x2  = 2y2
x  = 5 - y

x = _______
y = _______

CORRECT ANSWER
 xy
3.5
-1
2.5
-3
  • Question 6

Select one solution to this pair of simultaneous equations:

 

xy  = 5
2x - y = 9

x = _______
y = _______

CORRECT ANSWER
 xy
1
3
5
7
  • Question 7

Solve the following simultaneous equations:

18 - y2 = x2
y = 6 - x

x = _______
y = _______

CORRECT ANSWER
 xy
1
2
3
4
  • Question 8

Select one solution to this pair of simultaneous equations:

 

18 - 3y2 = -x
 y = 6 - x

x = _______
y = _______

CORRECT ANSWER
 xy
1
2
3
4
  • Question 9

Select one solution to this pair of simultaneous equations:

 

25 - 2x2 = y- 9
  x = 7 - y

x = _______
y = _______

CORRECT ANSWER
 xy
1.5
2.5
3
4
  • Question 10

Select one solution to this pair of simultaneous equations:

 

x = 3
y

y = 3x − 8 

x = _______
y = _______

CORRECT ANSWER
 xy
1
2
3
4
---- OR ----

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