Question

1. higher order thinking determine the number of solutions for this system of equations by inspection only. explain.

$3x + 4y = 17$
$21x + 28y = 109$

Explanation:

Step1: Scale first equation by 7

Multiply $3x + 4y = 17$ by 7:
$7(3x + 4y) = 7\times17$
$21x + 28y = 119$

Step2: Compare to second equation

Second equation: $21x + 28y = 109$
We now have two equations:
$21x + 28y = 119$ and $21x + 28y = 109$
These state the same left-hand side equals two different constants, which is a contradiction.

Answer:

This system has 0 solutions (no solution). The two equations represent parallel, non-intersecting lines because when scaling the first equation to match the coefficients of the second, the constant terms are inconsistent, making the system impossible to satisfy.