Question

12x + 15y = 9−12x − 18y = −6 PLEASE I NEED EXPLANATION THANKS

Answer 1

Answer:

x = 2

y = –1

Step-by-step explanation:

We need to solve this system of equations for the point where the two linear equations intersect. That means solving for one variable, then using that to solve for the other. But, I'm looking at this, and...

Well, I see an easy way to isolate y right now! See how one equation has 12x and the other has –12x? Adding the two equations together will cancel them out!

That gives us this equation:

12x – 12x + 15y – 18y = 9 – 6  — adding the expressions together

15y – 18y = 9 – 6  — cancel out the 12x

–3y = 3  — simplify the equation

–3y ÷ 3 = 3 ÷ 3  — divide by 3 to isolate y

y = –1  — simplify the equation

Now that we have our y-value, we can substitute into the equation and solve for x. I'm substituting into both to make sure y = –1 is part of the solution point (on a coordinate plane, this is where the functions intersect).

12x + 15y = 9  — original equation

12x + 15(–1) = 9  — substitute –1 for y

12x – 15 = 9  — simplify

12x – 15 + 15 = 9 + 15  — add 15 on both sides to isolate 12x

12x = 24  — simplify

12x ÷ 12 = 24 ÷ 12   — divide by 12 on both sides to isolate x

x = 2  — simplify

That's one equation. Let's check the other with these values to make sure (2, –1) is the solution point.

–12x – 18y = –6

–12(2) – 18(–1) ≟ –6

18 – 24 ≟ –6

–6 = –6 ✓

Yep, this is the solution we're looking for!

Hope this helps you understand the concept! Have a great day!