Substitution Method to solve linear simultaneous equation

In summary, the Substitution Method is a technique used to solve a system of linear equations by solving one of the equations for one of the variables and substituting it into the other equation. It is often used when the equations are in the form of "y = mx + b" or have coefficients that are easy to eliminate. The steps for using this method include solving, substituting, and solving again for the remaining variable. One of the advantages of this method is that it can be used for systems with any number of variables and allows for the elimination of one variable. However, it may not be the most efficient method for equations with large coefficients and may not work if the equations cannot be easily solved for one of the variables.
  • #1
Yazan975
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View attachment 8419

What I have done:

I changed all fractions to common denom and that gave me

5y-5x=1 (1) *I numbered the fractions
5y+2x=5 (2)

Then: 5y=5-2x

Substitute into equation 1
(5-2x)-5x=1
5-7x=1
x=4/7

Thing is my answer says I should be getting x=0

Any hints?
 

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  • #2
When you multiply the first equation by $6$ and simplify, you should get $y-5x=1$.
 

What is the Substitution Method?

The Substitution Method is a technique used to solve a system of linear equations. It involves solving one of the equations for one of the variables, and then substituting that expression into the other equation. This allows for the elimination of one variable, making it easier to solve for the remaining variable.

When is the Substitution Method used?

The Substitution Method is often used when the equations in the system are in the form of "y = mx + b". It can also be used when the equations have coefficients that are easy to eliminate.

What are the steps for using the Substitution Method?

The steps for using the Substitution Method are as follows:

  1. Solve one of the equations for one of the variables.
  2. Substitute the expression from step 1 into the other equation.
  3. Solve the resulting equation for the remaining variable.
  4. Substitute the value found in step 3 into either of the original equations to solve for the other variable.
  5. Check the solution by plugging the values into both original equations.

What are the advantages of using the Substitution Method?

One advantage of using the Substitution Method is that it can be used for systems of equations with any number of variables. It also allows for the elimination of one variable, making it easier to solve for the remaining variable.

Are there any limitations to using the Substitution Method?

The Substitution Method may not be the most efficient method for solving a system of equations, especially if the equations have large coefficients. It also may not work if the equations cannot be easily solved for one of the variables.

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