Answer:
<u><em>x</em></u><u> = 2</u>
<em><u>y</u></em><u> = –1</u>
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 <em>one</em> variable, then using that to solve for the other. But, I'm looking at this, and...
Well, I see an easy way to isolate <em>y</em> right now! See how one equation has <u>12</u><em><u>x</u></em> and the other has <u>–</u><u>12</u><u><em>x</em></u>? Adding the two equations together will cancel them out!
That gives us this equation:
12<em>x</em> – 12<em>x</em> + 15<em>y</em> – 18<em>y</em> = 9 – 6 — adding the expressions together
15<em>y</em> – 18<em>y</em> = 9 – 6 — cancel out the 12<em>x</em>
–3<em>y</em> = 3 — simplify the equation
–3<em>y</em> ÷ 3 = 3 ÷ 3 — divide by 3 to isolate <em>y</em>
<em>y</em> = –1 — simplify the equation
Now that we have our <em>y</em>-value, we can substitute into the equation and solve for <em>x</em>. I'm substituting into both to make sure <em>y</em> = –1 is part of the solution point (on a coordinate plane, this is where the functions intersect).
12<em>x</em> + 15<em>y</em> = 9 — original equation
12<em>x</em> + 15(–1) = 9 — substitute –1 for <em>y</em>
12<em>x</em> – 15 = 9 — simplify
12<em>x</em> – 15 + 15 = 9 + 15 — add 15 on both sides to isolate 12<em>x</em>
12<em>x</em> = 24 — simplify
12<em>x</em> ÷ 12 = 24 ÷ 12 — divide by 12 on both sides to isolate <em>x</em>
<em>x</em> = 2 — simplify
That's <em>one</em> equation. Let's check the other with these values to <em>make sure</em> (2, –1) is the solution point.
–12<em>x</em> – 18<em>y</em> = –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!
