Given the system of equations below:
[tex] \large{ \begin{cases} x + 2y = 12 \\ x = y - 12 \end{cases}}[/tex]
For the second equation, x-term is isolated and can be substituted in the first equation.
[tex] \large{(y - 12) + 2y = 12}[/tex]
The equation above is when we substitute x = y-12 in the first equation. Cancel the brackets.
[tex] \large{y - 12 + 2y = 12}[/tex]
Add up the like term and isolate y-term.
[tex] \large{3y - 12= 12} \\ \large{3y - 12 + 12 = 12 + 12}[/tex]
Add both sides by 12 to get rid of 12 from the left side to isolate y-term.
[tex] \large{3y = 24}[/tex]
Divide both sides by 3 so we can finally isolate the term.
[tex] \large{ \frac{3y}{3} = \frac{24}{3} } \\ \large{ \frac{ \cancel{3}y}{ \cancel{3}} = \frac{ \cancel{24}}{ \cancel{3}} } \\ \large{y = 8}[/tex]
Next, find the x-value because in system of equations - we have to answer as in an ordered pairs or coordinate point. We know y-value now but we don't know x-value yet. To find x-value, we substitute the y-value in one of two equations that are given. You can substitute in both equation but it's not necessary to substitute in both equations at one. I will choose to substitute in x = y-12.
[tex] \large{x = y - 12}[/tex]
Substitute y = 8 in the equation.
[tex] \large{x = 8 - 12} \\ \large{x = - 4}[/tex]
Now that we know the both values. We finally have an answer to this problem. Hence.
Answer
The second answer is in ordered pair form. Let me know if you have any doubts!
