Write as a Vector Equality y=3x-13 , 6x+3y=21

Problem

{[y=3*x−13],[6*x+3*y=21])

Solution

1. Rearrange the first equation into standard form A*x+B*y=C by subtracting 3*x from both sides.

−3*x+y=−13

2. Identify the coefficients of x and y from both equations to form the coefficient matrix and the constant vector.

Equation 1: −3*x+1*y=−13

Equation 2: *6*x+3*y=21

3. Express the system as a linear combination of vectors by grouping the terms containing x and the terms containing y

x*[[−3],[6]]+y*[[1],[3]]=[[−13],[21]]

4. Verify the vector equality by performing scalar multiplication and vector addition to ensure it matches the original system.

[[−3*x],[6*x]]+[[y],[3*y]]=[[−3*x+y],[6*x+3*y]]

Final Answer

x*[[−3],[6]]+y*[[1],[3]]=[[−13],[21]]

Want more problems? Check here!