Solving a System of Equations by Substitution

The first step is to solve one of the equations in the system for one of the variables. Which equation and variable do you think we should choose?

1) -2x + y = 6

2) 3x - 2y = 4

Let's solve equation 1 for y. We can do this one of two ways. Which of the following will work to do that (select two)?

What property allows us to add the same number to both sides of an equation?

1) -2x + y = 6

2) 3x - 2y = 4

Let's solve equation 1 for y. What do you get when you add 2x to both sides of the equation?

Next, we need to combine like terms on both sides of the equation. For this problem, we only have like terms on the left side, 3x and -4x. What do we get when we combine them?

Our equation now looks like this:

-x - 12 = 4

Now we want to move all the constant terms to the right side of the equals sign. How do we do this (select two)?

So now we know what negative x equals, but we are looking for the value of x. To determine the value of x, we can now either multiply both sides of the equation by -1, or divide both sides by -1. When we do this, what do we get for the value of x?

Now we need to figure out the value of the y coordinate in our solution. To do that, we will replace the x in one of our equations with the value we just got to get a single variable equation, which we then solve for y. Since we already solved one of the equations for y, it will be easiest to use that one, but you could also use either of the two original equations.

1) -2x + y = 6 or y = 2x + 6

2) 3x - 2y = 4

What single-variable equation do you get when you put in the known value of x?

Simplify the equation you found in question 11. What is the value of y?

Put the value you found for x and y into the original equation 1. Do you get a true statement?

Put the value you found for x and y into the original equation 2. Do you get a true statement?