In system equations, equivalent systems are systems that have the same solution. This means that if you solve one system, you can use the same solution for the other system.
To make equivalent systems, you can use operations that do not change the solution of the system. These operations include:
Swapping two equations Multiplying or dividing an equation by a non-zero number Adding or subtracting a multiple of one equation to another equation For example, let's say we have the system of equations:
2x + 3y = 7 x - 2y = 4
We can make an equivalent system by multiplying the second equation by 2:
2x + 3y = 7 2x - 4y = 8
Now we can add the two equations together to eliminate the x variable:
5y = 15
Finally, we can solve for y:
y = 3
We can then substitute this value of y into one of the original equations to solve for x:
2x + 3(3) = 7 2x + 9 = 7 2x = -2 x = -1
Therefore, the solution to the original system of equations is x = -1 and y = 3.