Math  /  Algebra

Question2) 2x3y=12 x-3 y=-1

Studdy Solution

STEP 1

What is this asking? We need to solve for xx *and* yy but we only have one equation!
This means there are infinitely many solutions, and we need to express one variable in terms of the other.
Let's write yy in terms of xx! Watch out! Don't forget that when we move terms to the other side of the equation, we need to flip the sign.
Also, remember to divide *all* terms by the same number when isolating a variable.

STEP 2

1. Isolate the term with yy.
2. Isolate yy.

STEP 3

We're starting with 2x3y=12x - 3y = -1.
This is our **starting point**!

STEP 4

We want to get the yy term by itself, so let's add 3y3y to both sides of the equation: 2x3y+3y=1+3y2x - 3y + 3y = -1 + 3y 2x=3y12x = 3y - 1See how the 3y-3y disappears from the left side because we added 3y3y to it?
That's adding to zero!

STEP 5

Now, let's add 1 to both sides to move the 1-1 away from the yy term: 2x+1=3y1+12x + 1 = 3y - 1 + 1 2x+1=3y2x + 1 = 3yGreat! We have isolated the term with yy!

STEP 6

To get yy completely by itself, we need to divide both sides of the equation by **3**: 2x+13=3y3\frac{2x + 1}{3} = \frac{3y}{3} 2x+13=y\frac{2x + 1}{3} = yRemember, dividing by **3** is the same as multiplying by 13\frac{1}{3}.
Since 133=1\frac{1}{3} \cdot 3 = 1, we are left with just yy on the right side!

STEP 7

We can rewrite the equation with yy on the left side: y=2x+13y = \frac{2x + 1}{3} And there we go!
We've expressed yy in terms of xx!

STEP 8

The solution is y=2x+13y = \frac{2x + 1}{3}.

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