Write as a Vector Equality -2y+12=7x , 5x+3y=18

Problem

−2*y+12=7*x,5*x+3*y=18

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by adding 2*y to both sides and swapping the sides.

7*x+2*y=12

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

A=[[7,2],[5,3]]

3. Identify the variables and the constants from the right-hand side of the equations.

x=[[x],[y]]

b=[[12],[18]]

4. Construct the vector equality by expressing the system in the form x*(v_1)+y*(v_2)=b where (v_1) and (v_2) are the columns of the coefficient matrix.

x*[[7],[5]]+y*[[2],[3]]=[[12],[18]]

Final Answer

x*[[7],[5]]+y*[[2],[3]]=[[12],[18]]

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