## Frequently Asked Questions on Simultaneous Equations

### What are simultaneous equations?

Simultaneous equations are sets of two equations that must be solved together.

In other words, simultaneous equations are two equations involving two unknowns.

These two unknowns must have the same values in both equations.

### What is the meaning of solutions of a pair of simultaneous equations?

The solution to a pair of simultaneous equations is the values of the two unknowns, say x and y, which satisfy the pair of simultaneous equations.

In other words, the solution of a pair of simultaneous equations is a set of values for the two unknowns that makes the pairs of equations true at the same time.

### How do you solve simultaneous equations?

You can solve simultaneous equations using four methods, namely; the substitution method, elimination method, Cramer rule, and graphical method.

The best method to use in solving a pair of simultaneous equations will depend on the specific equations and the required solution.

### What is the substitution method for solving simultaneous equations?

The substitution method of solving simultaneous equations involves making one of the variables the subject of the formula in one equation and then substituting the value into the other equation to solve for the other variable.

The resulting value of the other variable will then be substituted back into one of the original equations to solve for the remaining variable.

To know more about the substitution method of simultaneous equations, refer to this post.

### What is the elimination method for solving simultaneous equations?

True to its name, the elimination method of solving simultaneous equations try to eliminate one of the variables by adding or subtracting both equations so that the other variable can be derived.

To be able to eliminate one of the variables when we add or subtract the equations, we have to multiply one or both equations by constants so that one of the variables will be the same and ready for elimination.

After multiplying both equations by constants, you will then add or minus both equations.

The resulting equation will be a single equation with only one variable, which can then be solved using the normal method of solving one variable equation.

Refer to this post to know more about the elimination method of solving simultaneous equations.

### How do you know if pairs of simultaneous equations have no solution?

A simultaneous equation has no solution when there are sets of values that can satisfy all of the equations at the same time.

The two signs that show a pair of simultaneous equations have no real solutions are:

- The simultaneous equation has no real solutions when solving using the elimination or substitution method.
- The resulting values of the variables are not feasible.