How do you solve 9x+6y=3 and -3x+y=14 using substitution?

1 Answer
Jun 1, 2018

First, you take 1 equation and you make it so that the y is the main thing like y =something... Then you take that and you substitute it into your other equation to get x = something...You then take that and you substitute it into your first equation and done.

Explanation:

NOTE:
color color(gold)(gold and the bolded text is the main stuff
Other writing is explanations

So, to start you got these 2 equations...
color(gold)(9x + 6y = 3
color(gold)(-3x + y = 14

Let's call equation 1 A and equation 2 B. So...
9x + 6y = 3: color(red)(A
-3x + y = 14: color(blue)(B

So to start substituting, you first take color(blue)(B because it has the lowest number of 'y's...
-3x +y = 14 color(blue)(B
9x + 6y = 3 color(red)(A
Equation color(blue)(B has the lowest number of y.

Now, you take equation color(blue)(B and you twist and turn it to make the y in the equation the main letter. Like so...

color(gold)(-3x + y = 14 | This is your starting equation
y = 14 + 3x | you move over the '-3x' to the other side of the '=' sign. Since it was a 'negative' number before, going over to the other side makes '-3x' a positive number, '3x'.
color(gold)(y = 14 + 3x | now 'y' is the main letter.

Now you have this, you get your other equation (equation color(red)(A) and you 'combine' it with your new equation color(blue)(B. Like so...

9x + 6y = 3: color(red)(A
y = 14 + 3x: NEW color(blue)(B

You substitute your NEW color(blue)(B into color(red)(A...
9x+ 6color(gold)((14 + 3x)) = 3 | In the NEW color(blue)(B, it says the y = 'that'. Therefore, you can make the y in color(red)(A (6y) also equal 'that'.

Now you just have to do some switch-a-roos and stuff to get your answers: x = something and y = something, like this...

color(gold)(9x + 6(14 + 3x) = 3 | what you got now
9x + 84 + 18x = 3 | expanded the brackets
27x + 84 = 3 | added the similar numbers
27x = 3 - 84 | moved 84 to the other side
27x = -81
x = -81/27 | moved 27 to the other side.
color(gold)(x = -3 | your first answer.

Now...
color(gold)(-3x + y = 14: color(blue)(B | The old equation color(blue)(B
Since x = -3 so...
-3(-3) + y = 14 | substituting x = -3
9 + y = 14
y = 14 - 9 | moving 9 to the other side
color(gold)(y = 5 | your second answer.

That's how you do it.