Question

Solving system by substitution

Answer 1

Given the system of equations below:

$\large{ \begin{cases} x + 2y = 12 \\ x = y - 12 \end{cases}}$

For the second equation, x-term is isolated and can be substituted in the first equation.

$\large{(y - 12) + 2y = 12}$

The equation above is when we substitute x = y-12 in the first equation. Cancel the brackets.

$\large{y - 12 + 2y = 12}$

Add up the like term and isolate y-term.

$\large{3y - 12= 12} \\ \large{3y - 12 + 12 = 12 + 12}$

Add both sides by 12 to get rid of 12 from the left side to isolate y-term.

$\large{3y = 24}$

Divide both sides by 3 so we can finally isolate the term.

$\large{ \frac{3y}{3} = \frac{24}{3} } \\ \large{ \frac{ \cancel{3}y}{ \cancel{3}} = \frac{ \cancel{24}}{ \cancel{3}} } \\ \large{y = 8}$

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.

$\large{x = y - 12}$

Substitute y = 8 in the equation.

$\large{x = 8 - 12} \\ \large{x = - 4}$

Now that we know the both values. We finally have an answer to this problem. Hence.

Answer

• x = -4, y = 8
• (-4,8)

The second answer is in ordered pair form. Let me know if you have any doubts!

Answer 2

1. let’s solve for x.

x+2y=12

step 1: add -2y to both sides.

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

x = -2y + 12

answer: x = -2y + 12