shifa said:

what is the value of the y-coordinate of the solution to the system of equations x-2y=1 and x+4y=7

Some might think that graphing the two equations on the same coordinate axes, and finding the point of intersection, is the easiest way to find the solution, but many would disagree. For one thing, graphing takes some time...AND, more importantly, it is not always easy to find an accurate solution from a graph, since the point of intersection is USUALLY not easy to find.

There are a couple of ways to solve a system of equations algebraically....an algebraic solution will ALWAYS give you an accurate solution.

You've got

x - 2y = 1

x + 4y = 7

One way to solve this system is by the method of substitution. You can solve one of the equations for one variable in terms of the other variable.

For example, if you take the first equation,

x - 2y = 1

you can solve for x in terms of y. Add 2y to both sides of that equation, and you'll get

x = 1 + 2y

NOW...this tells you that "x" is the same thing as "1 + 2y"....so you can replace (substitute!) 1 + 2y for x in the second equation:

x + 4y = 7

(1 + 2y) + 4y = 7

You've now got an equation with just one variable....you should be able to solve this for the value of y.

1 + 2y + 4y = 7

1 + 6y = 7

6y = 6

y = 1

If y = 1, what is x? Well, we know that x = 1 + 2y. And if y = 1, x = 1 + 2(1), or y = 1 + 2, or x = 3.

So we have x = 3, and y = 1. Check. Are both the original equations TRUE when x = 1 and y = 3?

first equation: x - 2y = 1

If we substitute 3 for x and 1 for y, we have

3 - 2(1) = 1

3 - 2 = 1

1 = 1..........true, so that checks.

second equation: x + 4y = 7

If we substitute 3 for x and 1 for y, we have

3 + 4(1) = 7

3 + 4 = 7

7 = 7

That checks, too.

Since both equations are true when x = 3 and y = 1, we know that (3, 1) is the solution for the system.