Question

Find the value of x and y for the following equations
2x +3y =20
2x - y=12

• A. 8, 3
• B. 5, 2
• C. 2, 5
• D. 7, 2

Hint:

When the coefficients of one variable are the same or additive inverses, the elimination method is the quickest way to solve the system. Always verify your solution by plugging the values of x and y back into both original equations to ensure they hold true.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem involves solving a system of two linear equations with two variables (x and y). We can use methods like substitution, elimination, or matrix methods to find the unique solution. The elimination method is most straightforward here.

Step 2: Key Formula or Approach:
We will use the elimination method. The goal is to eliminate one variable by adding or subtracting the equations, allowing us to solve for the remaining variable.
Given equations:
Equation (1): \(2x + 3y = 20\)
Equation (2): \(2x - y = 12\)

Step 3: Detailed Explanation:
The coefficient of 'x' is the same in both equations (which is 2). Therefore, we can eliminate 'x' by subtracting Equation (2) from Equation (1).
\[ (2x + 3y) - (2x - y) = 20 - 12 \] \[ 2x + 3y - 2x + y = 8 \] \[ 4y = 8 \] \[ y = \frac{8}{4} = 2 \] Now that we have the value of y, we can substitute it back into either of the original equations to find x. Let's use Equation (2):
\[ 2x - y = 12 \] \[ 2x - (2) = 12 \] \[ 2x = 12 + 2 \] \[ 2x = 14 \] \[ x = \frac{14}{2} = 7 \] So, the solution is x = 7 and y = 2.

Step 4: Final Answer:
The values of x and y are 7 and 2, respectively. This corresponds to option (D).