a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
Here we have the system of equations:
(2/3)*x + (5/2)*y = 15
4x + 15y = 12
To solve the system of equations, we first need to isolate one of the variables in one of the equations, I will isolate x on the second equation.
4x = 12 - 15y
x = (12 - 15y)/4
Now we can replace that in the other equation:
(2/3)*x + (5/2)*y = 15
(2/3)* (12 - 15y)/4 + (5/2)*y = 15
Now we can solve that for y.
2 - (10/4)*y + (5/2)*y = 15
2 = 15
That is a false equation, then we conclude that the system of linear equations has no solutions.
This means that the two lines are parallel lines, then a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
Where a and b are two real numbers.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
