The GATE Grind

GATE 2016 ME (ME1) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Multiple choice

The system $\begin{bmatrix}2&5\\-4&3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}2\\-30\end{bmatrix}$ has solution $(x,y)$ ______.

  1. (6, 2)
  2. (−6, 2)
  3. (−6, −2)
  4. (6, −2)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) (6, −2)

Explanation

The system is2x+5y=2 and−4x+3y=−30. Twice the first equation plus the second gives13y=−26, so y=−2. Substitution gives2x−10=2, hence x=6. Thus **(6,−2), D**, satisfies both equations.