For a system of linear equations AX = B solved by Cramer's rule. if Delta_1 = 3, Delta_2 = 1, Delta_3 = 1 and 2x - y + 8z = 13 is one of the equations of the system then Delta=

The correct answer is Option 3. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Maths Q6 – AP-EAMCET 2026

← Back

Home Maths DeterminantsQuestion #158

For a system of linear equations

A X = B

solved by Cramer's rule. if

Δ_{1} = 3

Δ_{2} = 1

Δ_{3} = 1

and

2 x - y + 8 z = 13

is one of the equations of the system then

Δ =

Clue 1 of 3: Cramer's Rule

Remember the fundamental relationships between the variables ( $x, y, z$ ), the main determinant ( $Δ$ ), and the determinants formed by replacing coefficient columns with constant terms ( $Δ_{1}, Δ_{2}, Δ_{3}$ ).

🧠 Full Solution Path

Step 1: Recall Cramer's Rule for variables✦ Active

For a system of linear equations solved by Cramer's Rule, the values of $x, y,$ and $z$ are given by:

x = \frac{Δ_{1}}{Δ}, y = \frac{Δ_{2}}{Δ}, z = \frac{Δ_{3}}{Δ}

💡 Teacher's Secret Hint

Remember that $Δ$ is the determinant of the coefficient matrix, and $Δ_{1}, Δ_{2}, Δ_{3}$ are determinants formed by replacing the respective coefficient columns with the constant terms.

Step 2: Substitute expressions into the given equation○ Expand

We are given one of the equations from the system: $2 x - y + 8 z = 13$ . Substitute the Cramer's Rule expressions for $x, y,$ and $z$ into this equation:

2 (\frac{Δ_{1}}{Δ}) - (\frac{Δ_{2}}{Δ}) + 8 (\frac{Δ_{3}}{Δ}) = 13

Multiply the entire equation by $Δ$ to clear the denominators:

2 Δ_{1} - Δ_{2} + 8 Δ_{3} = 13 Δ

💡 Teacher's Secret Hint

Ensure you correctly apply the coefficients to the respective $Δ_{i}$ terms during substitution.

Step 3: Substitute given values and solve for

Δ

○ Expand

We are given the values: $Δ_{1} = 3$ , $Δ_{2} = 1$ , and $Δ_{3} = 1$ . Substitute these values into the equation from Step 2:

2 (3) - (1) + 8 (1) = 13 Δ

Perform the arithmetic operations:

6 - 1 + 8 = 13 Δ

5 + 8 = 13 Δ

13 = 13 Δ

Solve for $Δ$ :

Δ = \frac{13}{13} = 1

Step 4: Compare with options○ Expand

Now, let's evaluate each option using the given values of $Δ_{1}, Δ_{2}, Δ_{3}$ :

1. $Δ_{1} + Δ_{2} = 3 + 1 = 4$

2. $Δ_{1} + Δ_{2} + Δ_{3} = 3 + 1 + 1 = 5$

3. $Δ_{1} - Δ_{2} - Δ_{3} = 3 - 1 - 1 = 1$

4. $\frac{Δ_{1}}{Δ_{2}} = \frac{3}{1} = 3$

The calculated value of $Δ = 1$ matches option 3.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Maths Question 6 – AP-EAMCET 2026

Clue 1 of 3: Cramer's Rule

🧠 Full Solution Path