Solve 2x + 3y = 6
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | y = 2 − 2x/3 |
Step-by-step solution
5 steps-
1 Given2 x + 3 y = 6
Solve for y.
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2 Subtract 2x from both sides
An equation stays true as long as you do the same thing to both sides, like adding the same weight to both pans of a balance. Adding or subtracting the same amount on both sides moves a term to the other side, where it appears with the opposite sign.
3 y = 6 - 2 xMove the constant terms to the right.
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3 Divide both sides by 3
Dividing both sides by 3 undoes the multiplication by 3, so the variable is left on its own. Both sides change in the same way, so the equation stays true (dividing by 0 is the one thing that is never allowed).
y = \frac{6 - 2 x}{3} -
4 Simplifyy = 2 - \frac{2 x}{3}
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5 Read off the slope m and the y-intercept b from y = mx + bm = - \frac{2}{3},\quad b = 2
Table of values
| x | y |
|---|---|
| −2 | 10/3 |
| −1 | 8/3 |
| 0 | 2 |
| 1 | 4/3 |
| 2 | 2/3 |
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