Question

2x + 3y = 5
3x - 3y = 10
Which of the following best describes the solution set to the equation shown above?

• A. The equation has no solutions.
• B. The equation has exactly one solution, x = 3 , $y=-\frac{1}{3}$
• C. The equation has exactly one solution, x = 5, ,$y=\frac{1}{2}$
• D. The equation has infinitely many solutions.

Answer 1

The correct option is B The equation has exactly one solution, x = 3 , $y=-\frac{1}{3}$

Let us use elimination method to solve the above system of equations.
2x + 3y = 5
3x - 3y = 10
By adding the two equations we can eliminate the variable y.
2x + 3y = 5
3x - 3y = 10
____________
5x = 15
or , x = $\frac{15}{5}$
x = 3
Substitute the value of x in any of the two equations to get the value of y as follows :
2(3) + 3y = 5
6 + 3y = 5
3y = -1
y = $\frac{-1}{3}$
the correct answer is B