Express $y$ in terms of $x$ for the equation $2 x + 3 y = 12$ .

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

Move

2 x

across:

3 y = 12 - 2 x

, then divide the WHOLE right side by 3 →

y = (12 - 2 x) /3

. Check with

x = 3 : y = 6/3 = 2

, and

2 (3) + 3 (2) = 12

✓.

Answer: C)

y = (12 - 2 x) /3

Pick any value for one variable; solve for the other. Repeat to get many solutions.

Example:

3 x + 2 y = 12

.
- Let

x = 0 : 2 y = 12

→

y = 6

. So (0, 6) is a solution (this is the

y

-intercept).
- Let

x = 2 : 6 + 2 y = 12

→

y = 3

. So (2, 3) is a solution.
- Let

x = 4 : 12 + 2 y = 12

→

y = 0

. So (4, 0) is a solution (this is the

x

-intercept).
- Let

y = 0 : 3 x = 12

→

x = 4

. Same as above.

Four solutions found in seconds, and infinitely more available.

Don't just memorise the answer — build a daily practice habit.