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Algebra

Simulteneous Equations

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Simulteneous Equations Score: 0/10

1. Solve for x and y simultaneously :  

   y = 3x - 9  and  x 2 - 4x + y 2 + 6y = 77

A.( x ; y ) = ( − 12 ; − 1 )  and  ( x ; y ) = ( 6 ; 5 )
B.( x ; y ) = ( − 1 ; − 12 )  and  ( x ; y ) = ( 5 ; 6 )
C.( x ; y ) = ( 1 ; 12 )  and  ( x ; y ) = ( - 5 ; - 6 )
D. None of the above

2. Solve for x and y simultaneously :  

   y = - 3x + 2  and  ( x + 1 ) ( y + 2 ) = - 6

A.( x ; y ) = ( - 5 3  ; 7 )  and  ( x ; y ) = ( 2 ; - 4 )
B.( x ; y ) = ( - 3 5  ; 7 )  and  ( x ; y ) = ( 2 ; - 4 )
C.( x ; y ) = ( − 5 ; − 7 )  and  ( x ; y ) = ( 2 ; 4 )
D. None of the above

3. Solve for x and y simultaneously :  

   2y = 2x + 14  and  x 2 + 8x + y 2 − 4y = 41

A.( x ; y ) = ( 10 ; 3 )  and  ( x ; y ) = ( - 1 ; - 8 )
B.( x ; y ) = ( − 3 ; − 10 )  and  ( x ; y ) = ( 8 ; 1 )
C.( x ; y ) = ( − 10 ; − 3 )  and  ( x ; y ) = ( 1 ; 8 )
D. None of the above

4. Solve for x and y simultaneously :  

   y + x + 3 = 0  and  x 2 - 2x + y 2 + 10y = 155

A.( x ; y ) = ( − 8 ; 5 )  and  ( x ; y ) = ( 11 ; - 14 )
B.( x ; y ) = ( 8 ; − 5 )  and  ( x ; y ) = ( - 11 ; 14 )
C.( x ; y ) = ( 5 ; - 8 )  and  ( x ; y ) = ( - 14 ; 11 )
D. None of the above

5. Solve for x and y simultaneously :  

   y = 13x - 3  and  x 2 - 14x + y 2 − 6y = 27

A.( x ; y ) = ( 0 ; 3 )  and  ( x ; y ) = ( - 1 ; - 10 )
B.( x ; y ) = ( 0 ; − 3 )  and  ( x ; y ) = ( 1 ; 10 )
C.( x ; y ) = ( - 3 ; 0 )  and  ( x ; y ) = ( 10 ; 1 )
D. None of the above

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Question 1 of 10

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Solutions

Simulteneous Equations Question 1 of 5
1. Solve for x and y simultaneously :  

   y = 3x - 9  and  x 2 - 4x + y 2 + 6y = 77

A.( x ; y ) = ( − 12 ; − 1 )  and  ( x ; y ) = ( 6 ; 5 )
B.( x ; y ) = ( − 1 ; − 12 )  and  ( x ; y ) = ( 5 ; 6 )
C.( x ; y ) = ( 1 ; 12 )  and  ( x ; y ) = ( - 5 ; - 6 )
D. None of the above
Correct Answer
Option B
Detailed Solution

Solution Details

Given y = 3x - 9  and  x 2 - 4x + y 2 + 6y = 77

•   y = 3x - 9   ........................ 1

   x 2 - 4x + y 2 + 6y = 77   ........................ 2

•   Substitute  1  into  2

   x 2 - 4x + ( 3x - 9 ) 2 + 6 ( 3x - 9 ) = 77

   x 2 - 4x + 9x 2 - 54x + 81 + 18x - 54 = 77

   10x 2 - 40x - 50 = 0

   x 2 - 4x - 5 = 0

   ( x + 1 ) ( x - 5 ) = 0

   ( x + 1 ) = 0     or     ( x - 5 ) = 0

∴   x = - 1     or    x = 5

•   Substitute the values of x into  1  to get the values of y


   y = 3x - 9


   For   x = - 1

   y = 3 ( - 1 ) - 9 = - 12


   For   x = 5

   y = 3 ( 5 ) - 9 = 6

∴   ( x ; y ) = ( - 1 ; - 12 )  and

    ( x ; y ) = ( 5 ; 6 )

For more info please see

Simulteneous Equations

Simulteneous Equations Question 2 of 5
2. Solve for x and y simultaneously :  

   y = - 3x + 2  and  ( x + 1 ) ( y + 2 ) = - 6

A.( x ; y ) = ( - 5 3  ; 7 )  and  ( x ; y ) = ( 2 ; - 4 )
B.( x ; y ) = ( - 3 5  ; 7 )  and  ( x ; y ) = ( 2 ; - 4 )
C.( x ; y ) = ( − 5 ; − 7 )  and  ( x ; y ) = ( 2 ; 4 )
D. None of the above
Correct Answer
Option A
Detailed Solution

Solution Details

Given y = - 3x + 2  and  ( x + 1 ) ( y + 2 ) = - 6

•   y = - 3x + 2   ........................ 1

   ( x + 1 ) ( y + 2 ) = - 6   ........................ 2

•   Substitute  1  into  2

   ( x + 1 ) ( - 3x + 2 + 2 ) = - 6

   ( x + 1 ) ( - 3x + 4 ) = - 6

   - 3x 2 + x + 4 = - 6

   - 3x 2 + x + 10 = 0

   3x 2 - x - 10 = 0

   ( 3x + 5 ) ( x - 2 ) = 0

   ( 3x + 5 ) = 0     or     ( x - 2 ) = 0

∴   x = - 5 3     or    x = 2

•   Substitute the values of x into  1  to get the values of y


   y = - 3x + 2


   For   x = - 5 3

   y = - 3 ( - 5 3 ) + 2 = 7


   For   x = 5

   y = - 3 ( 2 ) + 2 = - 4

∴   ( x ; y ) = ( - 5 3  ;  7 )  and

    ( x ; y ) = ( 2 ; - 4 )

For more info please see

Simulteneous Equations

Simulteneous Equations Question 3 of 5
3. Solve for x and y simultaneously :  

   2y = 2x + 14  and  x 2 + 8x + y 2 − 4y = 41

A.( x ; y ) = ( 10 ; 3 )  and  ( x ; y ) = ( - 1 ; - 8 )
B.( x ; y ) = ( − 3 ; − 10 )  and  ( x ; y ) = ( 8 ; 1 )
C.( x ; y ) = ( − 10 ; − 3 )  and  ( x ; y ) = ( 1 ; 8 )
D. None of the above
Correct Answer
Option C
Detailed Solution

Solution Details

Given 2y = 2x + 14  and  x 2 + 8x + y 2 − 4y = 41

•   2y = 2x + 14   ........................ 1

   x 2 + 8x + y 2 − 4y = 41   ........................ 2


•   From  1  we have

   y = x + 7   ........................ 3


•   Substitute  3  into  2

   x 2 + 8x + ( x + 7 ) 2 − 4 ( x + 7 ) = 41

   x 2 + 8x + x 2 + 14x + 49 − 4x − 28 = 41

   2x 2 + 18x − 20 = 0

   x 2 + 9x − 10 = 0

   ( x + 10 ) ( x - 1 ) = 0

   ( x + 10 ) = 0     or     ( x - 1 ) = 0

∴   x = - 10     or    x = 1

•   Substitute the values of x into  3  to get the values of y


   y = x + 7


   For   x = - 10

   y = - 10 + 7  = - 3


   For   x = 1

   y = 1 + 7 = 8

∴   ( x ; y ) = ( - 10 ; - 3 )  and

    ( x ; y ) = ( 1 ; 8 )

For more info please see

Simulteneous Equations

Simulteneous Equations Question 4 of 5
4. Solve for x and y simultaneously :  

   y + x + 3 = 0  and  x 2 - 2x + y 2 + 10y = 155

A.( x ; y ) = ( − 8 ; 5 )  and  ( x ; y ) = ( 11 ; - 14 )
B.( x ; y ) = ( 8 ; − 5 )  and  ( x ; y ) = ( - 11 ; 14 )
C.( x ; y ) = ( 5 ; - 8 )  and  ( x ; y ) = ( - 14 ; 11 )
D. None of the above
Correct Answer
Option A
Detailed Solution

Solution Details

Given y + x + 3 = 0  and  x 2 - 2x + y 2 + 10y = 155

•   y + x + 3 = 0   ........................ 1

   x 2 - 2x + y 2 + 10y = 155   ........................ 2


•   From  1  we have

   y = - x - 3   ........................ 3


•   Substitute  3  into  2

   x 2 - 2x + ( - x - 3 ) 2 + 10 ( - x - 3 ) = 155

   x 2 - 2x + x 2 + 6x + 9 - 10x - 30 = 155

   2x 2 - 6x - 176 = 0

   x 2 - 3x - 88 = 0

   ( x + 8 ) ( x - 11 ) = 0

   ( x + 8 ) = 0     or     ( x - 11 ) = 0

∴   x = - 8     or    x = 11

•   Substitute the values of x into  3  to get the values of y


   y = - x - 3


   For   x = - 8

   y = 8 - 3  = 5


   For   x = 11

   y = - 11 - 3 = - 14

∴   ( x ; y ) = ( - 8 ; 5 )  and

    ( x ; y ) = ( 11 ; - 14 )

For more info please see

Simulteneous Equations

Simulteneous Equations Question 5 of 5
5. Solve for x and y simultaneously :  

   y = 13x - 3  and  x 2 - 14x + y 2 − 6y = 27

A.( x ; y ) = ( 0 ; 3 )  and  ( x ; y ) = ( - 1 ; - 10 )
B.( x ; y ) = ( 0 ; − 3 )  and  ( x ; y ) = ( 1 ; 10 )
C.( x ; y ) = ( - 3 ; 0 )  and  ( x ; y ) = ( 10 ; 1 )
D. None of the above
Correct Answer
Option B
Detailed Solution

Solution Details

Given y = 13x - 3  and  x 2 - 14x + y 2 − 6y = 27

•   y = 13x - 3   ........................ 1

   x 2 - 14x + y 2 − 6y = 27   ........................ 2

•   Substitute  1  into  2

   x 2 - 14x + ( 13x - 3 ) 2 − 6 ( 13x - 3 ) = 27

   x 2 - 14x + 169x 2 − 78x + 9 − 78x + 18 = 27

   170x 2 - 170x = 0

   x 2 - x = 0

   x ( x - 1 ) = 0

   x = 0     or     ( x - 1 ) = 0

∴   x = 0     or    x = 1

•   Substitute the values of x into  1  to get the values of y


   y = 13x - 3


   For   x = 0

   y = 13x - 3 = - 3


   For   x = 1

   y = 13x - 3 = 10

∴   ( x ; y ) = ( 0 ; - 3 )  and

    ( x ; y ) = ( 1 ; 10 )

For more info please see

Simulteneous Equations