Solve the Matrix Equation [[2x+3y],[3x-y]]=[[7],[16]]

Problem

[[2*x+3*y],[3*x−y]]=[[7],[16]]

Solution

1. Set up the system of linear equations by equating the corresponding entries of the matrices.

2*x+3*y=7

3*x−y=16

2. Isolate the variable y in the second equation to prepare for substitution.

−y=16−3*x

y=3*x−16

3. Substitute the expression for y into the first equation.

2*x+3*(3*x−16)=7

4. Distribute the constant and combine like terms to solve for x

2*x+9*x−48=7

11*x−48=7

11*x=55

x=5

5. Substitute the value of x back into the expression for y

y=3*(5)−16

y=15−16

y=−1

Final Answer

[[2*x+3*y],[3*x−y]]=[[7],[16]]⇒x=5,y=−1

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