Understanding Simultaneous Solutions | What They Are and How to Find Them

Simultaneous Solution

A simultaneous solution refers to the set of values that satisfy multiple equations or inequalities at the same time

A simultaneous solution refers to the set of values that satisfy multiple equations or inequalities at the same time. In other words, it is the solution where all the given equations or inequalities are true simultaneously.

For example, consider the following system of equations:

1) 2x + y = 8
2) x – y = 4

To find the simultaneous solution for this system, we need to determine the values of x and y that satisfy both equations. We can do this using various methods such as substitution, elimination, or graphing.

One way to solve this system is by using the substitution method. From the second equation, we can express x in terms of y as follows: x = y + 4. Now, we substitute this value of x into the first equation:

2(y + 4) + y = 8
2y + 8 + y = 8
3y + 8 = 8
3y = 0
y = 0

Substituting this value of y back into the second equation, we can find the value of x:

x – 0 = 4
x = 4

So, the simultaneous solution for this system of equations is x = 4 and y = 0. This means that the point (4, 0) is the solution that satisfies both equations.

In general, a system of equations or inequalities can have one unique simultaneous solution, infinitely many solutions, or no solution at all, depending on the relationships between the equations.

More Answers: