### Solve a Simultaneous Equation with Examples

In this tutorial we will go through the simultaneous equations with examples. If there are two unknown variables, then we have to have two equations to find those two unknowns. Those kinds of equations called Simultaneous equations. Most of the time in grade 9 mathematics will cover the Simultaneous equations sections.

Simultaneous equations can be solve,
•     Elimination method
•     Substitution method
Elimination method

Ex:

4x + y = 9 ----------------- (1)
x – y = 1 ----------------- (2)

Step 1: Make the coefficients of the same in one of the variables in both equations. As you can see in the example variable “y” coefficients is 1 and -1. So we can simply eliminate “y” by adding two equations.

(1)    + (2)

4x + y + x – y = 9 + 1
5x = 10
x= 2

Now we can apply x in one of the equation (1 or 2), applying x for equation (1)

4 * 2 + y = 9
Y = 1

Now we can apply x and y in equations two and verify the results are fine.

Substitution method

This is more reliable method when solving hard questions.

Ex:

4x + y = 9 ----------------- (1)
x – y = 1 ----------------- (2)

Step 1: First define one variable from other variable in equation (1)

Y = 9 – 4x ----------------- (3)

Now apply equation (3) in equation (2)

x – y = 1
x – (9 – 4x) = 1
x - 9 + 4x = 1
5x = 10
x= 2

Apply x in equation (3)

y = 9 – 4*2
y = 1

Now verify your result applying in equation (1)

### Hard Mathematics Pattern IQ questions and Answers

Here are some mathematics pattern IQ questions that can really challenge your mind. Try this and check your answers. Hope you will enjoy…

Questions

Que 1.
6+3+5 = 183033
4+8+3= 321265
3+9+4= 271236

Then

5+6+5=??

Que 2.
1, 2, 6,42,1806, __ ?

Que 3.
0, 1, 4, 25, 676, __ ?

1.

6+3+5 = 18 30 33
4+8+3= 32 12 65
3+9+4= 27 12 36
p+q+r= A    B   C
A=p x q
B=p x r
C= p x q + q x r (then the answer is reversed ( 5x6 + 6x5 = 60, reversed is 06))

Ans: 302506

2.

1, 2, 6, 42, 1806, __?
A, B, C                X

B = A2 + A
C = B2 + B

Ans:  X = 18062 + 1806 = 3263442

3.

0, 1, 4, 25, 676, __ ?
A, B, C              X

B = A2 + A*2 + 1
C = B2 + B*2 + 1

Ans: X = 6762 + 676*2 + 1 = 458329

### Kinetic Energy Basic Questions and Answers

Kinetic energy is the energy of motion. If any object is moving, rotating that object contains kinetic energy. This tutorial we will briefly go through the kinetic energy basic questions. Importantly kinetic energy is scalar quantity, which means it does not have direction.

Equation:    Kinetic Energy = ½ * Mass of the Object * (Velocity) 2

E = ½ MV2

The unit of Kinetic Energy = J (Joule) = kg * (m/s) 2

Questions

1. Object “P” has Mass of 60 kg and velocity (speed) 120 ms-1 at point A. what is the kinetic energy at point A?

1. When object “P” moves to it has a Kinetic energy of 6000J, what is the velocity of the object “p” at point B?

1. Then in point C Object “P” moves in vertical direction with 20 ms-1 speed. What is the kinetic energy of object “p”?  In which direction?

1. Object P has a kinetic energy of 200J and object Q has a kinetic energy of 100J. Object Q has a velocity of 5 ms-1.  Object P’s mass is twice of the Object Q’s mass. What is the velocity of object P?

Graph for Ques 1,2,3

1. Applying, E = ½ MV2 at point A

E = ½ * 60 * (120) 2
E = 432000 J = 432 kJ

2. Applying, E = ½ MV2 at point B

6000 = ½ * 60 * V2
V = 14.14 ms-1

3. Applying, E = ½ MV2 at point C

E = ½ * 60 * (20) 2
E = 12000 J = 12 kJ
As kinetic energy is a scalar quantity, which don’t have direction.

4.
Applying, E = ½ MV2 for Object P

200 = ½ * mp * Vp2 ------------------------ A

Applying, E = ½ MV2 for Object Q

100 = ½ * mq * 52 ------------------------ B

Given that,

2 mqmp ------------------------ C

From above 3, A/B

2 = (mp / mq) * (Vp2 /  52 ) ------------------------ D

Applying (C) in above equation (D),

2 = (2 mq / mq) * (Vp2 /  52 )

Vp = 5 ms-1