Tracy A. answered • 11/07/12

Teacher Specializing in Math and Language Arts

Hi Ciera,

This can be solved in a couple of steps.

Do you know how to "isolate" a variable? You know, get a variable on one side by itself? This is step one. Choose one of the equations, doesn't matter which, and solve for one of the variables (doesn't matter which).

For Example, if you chose this equation: x - y = 2

You could solve for x by adding y to both sides. This would eliminate the y variable on the left side and add it to the right side... giving you this: x = 2 + y

Now you have isolated the variable, x.

Take your new equation, x = 2 + y and substitute this equation into the second equation.

Notice that the second equation has both x and y variables also: 4x - 3y = 11

You can replace (substitute) your first equation into the position of the 'x' in the second equation. Why? So that you will only have one variable in the second equation instead of two. Then you'll be able to solve the second equation and find out the value of y. It looks like this:

4x - 3y = 11

4(2 + y) - 3y = 11

Notice that every other part of the second equation remains the same. The only thing we changed was that we replaced the x variable with part of the first equation. Since x = 2 + y, we can substitute the x for 2 + y in the second equation.

Now we solve for y by following these steps: distribute, add like terms, and isolate the y variable. It looks like this:

Given: 4(2 + y) - 3y = 11

Distribute: 4(2) + 4y - 3y = 11

Multiply: 8 + 4y - 3y = 11

Combine like terms (4y - 3y = y): 8 + y = 11

Isolate the variable by subtracting the 8 from both sides: y = 11 - 8

Subtract: y = 3

Now that you know the value of y, you can substitute that value into the first equation to find the value of x.

x = 2 + y

x = 2 + 3

x = 5

The solution to the system of equations is x = 5 and y = 3

Written as a coordinate: (5, 3)