# Write a system of linear equations in two variables 6th

A solution for a system of equations is any point that lies on each line in the system.

Verify algebraically that your solution satisfies both equations. Because one of the variables had the same coefficient with opposite signs it will be eliminated when we add the two equations.

Find the solution by setting the two linear functions equal to another and solving for x, or find the point of intersection on a graph. The area to the left of the break-even point represents operating at a loss. Notice the results are the same.

## Linear equations in two variables questions

The total number of people is 2, And let's see, if y were to equal zero, if y were to equal zero then this is gonna be four times x is equal to twelve, well then x is equal to three. Make sure that one variable is positive and the other is negative before you add. So this is, this line is going to look something like-- something like, I'll just try to hand draw it. Now why do we call it a linear equation? It is quite possible that a mistake could result in a pair of numbers that would satisfy one of the equations but not the other one. This also is a linear equation. So when you go to add these two together they will drop out. This means we should try to avoid fractions if at all possible. So, for example the equation y is equal to two x minus three, this is a linear equation. That's why it's called a linear equation.

Once this is done substitute this answer back into one of the original equations. And we can see that if we were to graph the xy pairs that satisfy this we would once again get a line.

Notice that the two lines are parallel and will never intersect.

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