Algebra

Step 1: Write down the given pair of linear equations.
Equation 1: Equation 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.

Step 3: Substitute the value of x into one of the original equations to find y.
Using Equation 2: Substitute : So, the solution is .

Step 4: Verify the solution with Equation 1.
.
The solution is correct.
This matches option (4).

Step 1: Analyze the quadratic expression .
We need to find two numbers that: - Multiply to the constant term (-6).
- Add up to the coefficient of the x term (-1).

Step 2: Find the two numbers.
Pairs of factors for -6: - (1, -6) or (-1, 6) → Sums are -5 or 5.
- (2, -3) or (-2, 3) → Sums are -1 or 1.
The pair (2, -3) adds up to .

Step 3: Rewrite the middle term using these numbers and factor by grouping.
Group terms: Factor out common factors from each group: Factor out the common binomial factor :
Step 4: Verify by expanding the factored form.
.
The factorization is correct.
This matches option (2).