0Linear Equations In 2 Variables: Wordy Problems
A linear equation in 2 variables again is an equation of degree 1 but has 2 variables.
Example:
2x+3y=5, 3x/2 –y = 0.5
Generally, these are equations that one would have seen simultaneously (2 at a time), where solving for the values of the 2 variables involved processes like elimination or substitution.
Example:
Solve for x and y given the above 2 linear equations in 2 variables (in the example above)
Solution:
Elimination process involves multiplying the equation (2x+3y=5) with 3/4 so that the coefficients of x in both the equations equal each other.
3/4 (2x + 3y =5) implies 3x/2 + 9y/4 = 15/4. Now, as the coefficients of x in both the equations is the same, we can subtract one equation from another to eliminate x from them.
(3x/2 + 9y/4 = 15/4) – (3x/2 – y = 0.5) implies (9y/4+y = 15/4 -0.5) from which it can be implied that 13y/4 = 13/4. Hence y = 1. Substituting the value of y back into any of the equation we also get the value of x as 1.
The challenges in questions on the SAT math on this concept are generally about taking care of the signs in the equations. Most of the questions that test takers go wrong at are those in which care has to be taken in handling the signs (-, +) when doing the operations explained above.
