Question

Francis graphs the system of equations to determine its solution.

3x + 2y = 12
3x - y = 3

What is the correct solution?
A) x = 3, y = 3
B) x = 3, y = 0
C) x = 0, y = 3
D) x = 0, y = 0

Answer 1

The correct solution to the system of equations is x = 3, y = 0.

Step-by-step explanation:

The correct solution to the system of equations is option B) x = 3, y = 0.

To solve the system, we can either use the substitution method or the elimination method. Let's use the elimination method:

Multiply the second equation by 2 to make the y's terms cancel each other out:

6x - 2y = 6

Next, subtract the first equation from the modified second equation:

(6x - 2y) - (3x + 2y) = 6 - 12

Simplify the equation:

3x - 4y = -6

Now, we have a new system of equations:

3x + 2y = 12

3x - 4y = -6

By adding the two equations together, the y terms will cancel out:

(3x + 2y) + (3x - 4y) = 12 - 6

Simplify the equation:

6x - 2y = 6

Now, divide each term by 2 to get:

3x - y = 3

Both equations are the same as the original system. Since the equations are equivalent, the solution is the same as well, which is x = 3 and y = 0.