Question

What is the solution of the system? Solve using matrices. ( -3x + 2y = 10 -4x + 3y = 2 (-26 -34) (-34 -26) (26 34) O( no solution)

x + 2y = -1,, x-3y=-2
(-7 ,3)(3,-7) (7,-3)(no solution)
Inverse Matrices and Systems

Answer 1

(a) (-26, -34)

Explanation:

You want the solution to the system of equations ...

• -3x +2y = 10
• -4x +3y = 2

apparently using inverse matrices.

Matrix equation

The system can be represented by the matrix equation ...

AX = B

where A is the 2×2 matrix of coefficients, X is the 2×1 variable vector, and B is the 2×1 matrix of constants.

The solution to this system is found by multiplying on the left by the inverse of A:

A⁻¹·AX = A⁻¹·B

X = A⁻¹·B

The attachment shows the result of making this calculation:

`\boxed{X=\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}-26\\-34\end{array}\right]}`