Solve the first equation for :

Substitute into the second equation:

Multiply the entire equation by 2 to eliminate the fraction:

Using the value of , solve for :

Therefore, the solution is

Set the two equations equal to one another:

2x - 2 = 3x + 6

Solve for x:

x = -8

Plug this value of x into either equation to solve for y.  We'll use the top equation, but either will work.

y = 2 * (-8) - 2

y = -18

Multiply the bottom equation by , then add to the top equation:

Divide both sides by 

When we add the two equations, the  variables cancel leaving us with:

Solving for  we get:

We can then substitute our value for  into one of the original equations and solve for :

We are given

We can solve this by using the substitution method.  Notice that you can plug  from the first equation into the second equation and then get

Add  to both sides

Add 9 to both sides

Divide both sides by 5

So . We can use this value to find y by using either equation. In this case, I'll use .

So the solution is 

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination. 

Substitution can be used by solving one of the equations for either  or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the  form, and then set both equations equal to each other. 

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable. 

For this problem, elimination makes the most sense because our  variables have the same coefficient. We can add our equations together to cancel out the 

Next, we can divide both sides by  to solve for 

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both  and  values. 

Now that we have the value of , we can plug that value into the  variable in one of our given equations and solve for 

We want to subtract  from both sides to isolate the 

Our point of intersection, and the solution to the two system of linear equations is 

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination. 

Substitution can be used by solving one of the equations for either  or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the  form, and then set both equations equal to each other. 

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable. 

For this problem, elimination makes the most sense because our  variables have the same coefficient. We can subtract our equations to cancel out the 

Next, we can divide both sides by  to solve for 

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both  and  values. 

Now that we have the value of , we can plug that value into the  variable in one of our given equations and solve for 

We want to add  to both sides to isolate the 

Then we divide each side by 

Our point of intersection, and the solution to the two system of linear equations is 

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination. 

Substitution can be used by solving one of the equations for either  or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the  form, and then set both equations equal to each other. 

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable. 

For this problem, elimination makes the most sense because our  variables have the same coefficient. We can subtract our equations to cancel out the 

Next, we can divide both sides by  to solve for 

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both  and  values. 

Now that we have the value of , we can plug that value into the  variable in one of our given equations and solve for 

We want to subtract  from both sides to isolate the 

Then divide both sides by  to solve for 

Our point of intersection, and the solution to the two system of linear equations is 

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination. 

Substitution can be used by solving one of the equations for either  or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the  form, and then set both equations equal to each other. 

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable. 

For this problem, elimination makes the most sense because our  variables have the same coefficient. We can subtract our equations to cancel out the 

Next, we can divide both sides by  to solve for 

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both  and  values. 

Now that we have the value of , we can plug that value into the  variable in one of our given equations and solve for 

We want to subtract  from both sides to isolate the 

Then divide both sides by  to solve for 

Our point of intersection, and the solution to the two system of linear equations is 

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination. 

Substitution can be used by solving one of the equations for either  or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the  form, and then set both equations equal to each other. 

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable. 

For this problem, elimination makes the most sense because our  variables have the same coefficient. We can subtract our equations to cancel out the 

Next, we can divide both sides by  to solve for 

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both  and  values. 

Now that we have the value of , we can plug that value into the  variable in one of our given equations and solve for 

We want to subtract  from both sides to isolate the 

Our point of intersection, and the solution to the two system of linear equations is