A lnear combination of a system of equations can be obtained by adding/subtracting a multiple of the equations of the of the system.
Given the
system of equations
[tex] \frac{2}{3} x+ \frac{5}{2} y=15 \ \ \ \ \ \ \ \ (1) \\ \\ 4x+15y=12 \ \ \ \ \ \ \ \ (2)[/tex]
Now multiplying equation (1) by 6 and equation (2) by 1, we have:
[tex](1)\times6\Rightarrow4x+15y=90 \ \ \ \ \ \ \ \ (3) \\ \\ (2)\times1\Rightarrow4x+15y=12 \ \ \ \ \ \ \ \ (4)[/tex]
Subtracting equation (4) from equation (3) gives:
[tex]0=78[/tex]
Therefore, a system of linear equation that has no solution results on two unequal numbers in both sides of the equation.
Therefore, the equation that could represent a linear combination of the system is 0 = 26.
