Write as a Vector Equality y=4x+5 , -4x+y=-13

Problem

{[y=4*x+5],[−4*x+y=−13])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting 4*x from both sides.

−4*x+y=5

2. Identify the coefficients of the variables x and y to form the coefficient matrix and the constants to form the result vector.

Equation 1: −4*x+1*y=5

Equation 2: −4*x+1*y=−13

3. Express the system as a linear combination of vectors by using the coefficients of x as the first vector and the coefficients of y as the second vector.

x*[[−4],[−4]]+y*[[1],[1]]=[[5],[−13]]

Final Answer

x*[[−4],[−4]]+y*[[1],[1]]=[[5],[−13]]

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