Question

What is the solution to the system of equations? Use the substitution method.
y+2x=7
14-4x=2y

A. the solution is (1,5)
B. the solution is (21,0)
C. there is an infinite number of solutions
D. There is no solution

Answer 1

Try and use substitution. Here is an example: The substitution method is a method that is based off a rule of algebra. Basically, it's similar to using a formula. You substitute values into the formula. The same thing applies here.

Let's say we have the following system:

y = 2x + 3
5x + 2y = 24

Before we turn over to elimination, let's try using our new friend substitution. It clearly says that y is equal to 2x + 3. This means that we can substitute 2x + 3 in for y.

5x + 2y = 24
5x + 2(2x + 3) = 24
5x + 4x + 6 = 24

Now that we have eliminated a variable, we can solve the system.

9x + 6 = 24
9x = 18
x = 2

Now let's plug this back into one of the equations. I prefer to plug it into the equation that has a variable isolated.

y = 2x + 3
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the solution set is (x, y) = (2, 7).

Answer 2

Now try and do it yourself, you can follow the guidelines :)