Which equation could represent a linear combination of the system

Asked by maham237 @ 25/04/2021 in Mathematics viewed by 371 People

The system of equations below has no solution. 2/3x+5/2y=15 4x+15y=12 Which equation could represent a linear combination of the system? A) 4/3x=42 B)0=26 C)15/2y=33 D)0=0

Answered by maham237 @ 25/04/2021

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
$\frac{2}{3} x+ \frac{5}{2} y=15 \ \ \ \ \ \ \ \ (1) \\ \\ 4x+15y=12 \ \ \ \ \ \ \ \ (2)$

Now multiplying equation (1) by 6 and equation (2) by 1, we have:
$(1)\times6\Rightarrow4x+15y=90 \ \ \ \ \ \ \ \ (3) \\ \\ (2)\times1\Rightarrow4x+15y=12 \ \ \ \ \ \ \ \ (4)$

Subtracting equation (4) from equation (3) gives:
$0=78$

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.

Which equation could represent a linear combination of the system

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