How to solve simultaneous equation

1. Substitution: Substitute one equation into another to solve for a variable.

2. Elimination: Add or subtract the equations to eliminate one of the variables.

3. Gaussian elimination: Use row operations to convert the augmented matrix into reduced row-echelon form.

4. Cramer's rule: Express the solution in terms of determinants.Matrix inversion: Express the system as a matrix equation and find the inverse of the matrix.

Here are a few examples of how to solve simultaneous equations using different methods:

Substitution: Example: Solve for x and y in the system of equations: y = x + 2 y = -x + 6

Solution: Substitute the first equation into the second: -x + 6 = x + 2 Solve for x: -2x = 4 x = -2 Substitute x = -2 back into the first equation to find y: y = -2 + 2 = 0 So the solution is x = -2, y = 0.

Elimination: Example: Solve for x and y in the system of equations: 2x + y = 8 ---------(1)

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

Solution: Multiply the first equation by 2: 4x + 2y = 16

Subtract the second equation from the first:

3x = 10 Solve for x: x = 10/3

Substitute x = 10/3 back into the second equation to find y: 10/3 + 2y = 6

Solve for y: y = (6 - 10/3) / 2 = (6 - 10)/6 = -2/3

So the solution is x = 10/3, y = -2/3.

Comments

Volume of frustum and hemisphere

The volume of a frustum of a cone of height h is given by the V= 1/3*pi*h (R^2 +Rr +r^2), Where R and r are the radii of its circular ends. Hollow metal hemispheres of internal and external diameters 12.5cm and 17.5cm, respectively, are to be cast from the molten contents of a ladle in the shape of a frustum of a cone of depth 1.2 metres and radii of ends 0.6m and 0.675m. Calculate the number of hemispheres that can be cast. Solution To solve any problem in mathematics you have to read and understand the problem you are to solve, especially word problem related questions. Failure to carefully read the question might lead to wrong interpretation of the problem and the result of it will be wrong solution to the problem. All problems on this platform have been carefully solved and prepared. If you are a student looking for solutions to your assignments then you are at the right place. If you are an upcoming teacher looking for solution to a challenging question then you are als...

Solving Simultaneous equation using matrix method

Solving Simultaneous equation using matrix Method Question: Find the values of x and y in the equations below 3 x + 2 y = 6 5 x − y = 8 Using matrix method Put the equations in standard form and then use matrices to solve the system of equations. 3 x + 2 y = 6 , 5 x − y = 8 Write the equations in matrix form ( 3 5 2 − 1 ) ( x y ) = ( 6 8 ) Left multiply the equation by the inverse matrix of ( 3 5 2 − 1 ) . i n v e r s e ( ( 3 5 2 − 1 ) ) ( 3 5 2 − 1 ) ( x y ) = i n v e r s e ( ( 3 5 2 − 1 ) ) ( 6 8 ) The product of a matrix and its inverse is the identity matrix ( 1 0 0 1 ) ( x y ) = i n v e r s e ( ( 3 5 2 − 1 ) ) ( 6 8 ) Multiply the matrices on the left hand side of the equal sign. ( x y ) = i n v e r s e ( ( 3 5 2 − 1 ) ) ( 6 8 ) For the 2 × 2 matrix ( a c b d ) , the inverse matrix is ( a d − b c d a d − b c − c a d − b c − b a d − b c a ) , so the matrix equation can be ...

How to find the vertical angle of the cone.

A cone of height 9cm has a volume of ncm cube and a curved surface area of of ncm square. Find the vertical angle of the cone. SOLUTION

Tell Math

Search This Blog