Question

Which system of equations correspond to this matrix equation?

Question 9 options:
5x + 2x = -7
3y - 4y = -6

5x + 2y = -7
3x + 4y = -6

5x + 2y = -7
3x - 4y = -6

5x - 2y = -7
3x - 4y = -6

Answer 1

Answer: (C)

Explanation:

When multiplying matrices:

Row 1 x Column 1 = the value in Row 1 Column 1

• 
  `\left[\begin{array}{cc}5&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]= -7`
• ⇒ 5(x) + 2(y) = -7
• ⇒ 5x + 2y = -7

Row 2 x Column 1 = the value in Row 2 Column 1

• 
  `\left[\begin{array}{cc}3&-4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]= -6`
• ⇒ 3(x) + -4(y) = -6
• ⇒ 3x - 4y = -6

Combine the two equations to get:

`\left \{ {{5x + 2y = -7} \atop {3x - 4y = -6}} \right`

Answer 2

5x + 2x = -7

3y - 4y = -6

Explanation:

Given the matrix, we can multiply across the constant matrix and down the variable matrix

5x +2y = -7

3x -4y = -6