Final answer:
A solution to a system of equations means finding values for the unknown variables that make all of the equations true simultaneously. This is done by solving the system of equations, which involves manipulating the equations to eliminate variables until you can find the values of the unknowns.
Step-by-step explanation:
A solution to a system of equations means finding values for the unknown variables that make all of the equations true simultaneously. When you have more than one equation, you need to find values that satisfy all of the equations at the same time. This is done by solving the system of equations, which involves manipulating the equations to eliminate variables until you can find the values of the unknowns.
For example, let's say we have the following system of equations:
Equation 1: 2x + 3y = 10
Equation 2: x - 2y = 5
To find the solution, we can use various methods like substitution, elimination, or graphing. Let's use the elimination method:
Multiplying Equation 2 by 2 to eliminate x:
2(x - 2y) = 2(5)
Simplifying: 2x - 4y = 10
Now we have the following system with Equation 1 and the modified Equation 2:
Equation 1: 2x + 3y = 10
Modified Equation 2: 2x - 4y = 10
Subtracting Equation 1 from the modified Equation 2 to eliminate x:
(2x - 4y) - (2x + 3y) = 10 - 10
Simplifying: -7y = 0
From this equation, we see that y equals 0. Substituting this value back into Equation 1:
2x + 3(0) = 10
Simplifying: 2x = 10
This gives us x = 5. So, the solution to the system of equations is x = 5 and y = 0.