Solve this system of equations

One or more solutions:
ONo solution
O Infinite number of solutions

To solve the system of equations given by and , we can start by manipulating the second equation for clarity. Dividing the second equation by 3 gives us , which simplifies our view of the relationship between and .

From this equation, we can express in terms of : . Next, we substitute this expression for into the first equation :

This expands to , leading to . Solving for , we find or , thus .

We plug back into to get . So we find a unique solution: . Therefore, there is one solution to the system.

Now, you have a great foundation in solving systems of equations! To make your learning even more vibrant, you might want to check out some real-life applications: these systems actually model various scenarios, such as calculating costs or predicting outcomes in business or engineering!

Moreover, it’s quite easy to mix-up signs in algebraic manipulations – be sure to double-check your calculations when rearranging or substituting! Clearly keeping track of your steps can help you avoid common errors and boost your confidence in solving equations effectively!