Question

The solution for the pair of linear equations in two variables \(2x + y = 10, x - y = 2\); is

• A. \(x=2, y=4\)
• B. \(x=-2, y=4\)
• C. \(x=4, y=-2\)
• D. \(x=4, y=2\)

Hint:

To solve a system of two linear equations: - Elimination Method: Add or subtract the equations (after multiplying by constants, if necessary) to eliminate one variable. - Substitution Method: Solve one equation for one variable in terms of the other, then substitute that expression into the second equation. Always verify your solution by substituting the values back into the original equations.

Answer 1

The Correct Option is D

Step 1: Write down the given pair of linear equations.
Equation 1: \(2x + y = 10\) Equation 2: \(x - y = 2\)
Step 2: Solve the system of equations.
We can use the method of elimination or substitution.
Using elimination: Add Equation 1 and Equation 2.
\[ (2x + y) + (x - y) = 10 + 2 \] \[ 2x + x + y - y = 12 \] \[ 3x = 12 \] \[ x = \frac{12}{3} = 4 \]
Step 3: Substitute the value of x into one of the original equations to find y.
Using Equation 2: \(x - y = 2\) Substitute \(x=4\): \[ 4 - y = 2 \] \[ y = 4 - 2 = 2 \] So, the solution is \(x=4, y=2\).

Step 4: Verify the solution with Equation 1.
\(2x + y = 10\) \(2(4) + 2 = 8 + 2 = 10\).
The solution is correct.
This matches option (4).