As per linear equation, except for the option(4), all system of equations have same solution.
What is a linear equation?
"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, 'A' is a coefficient and 'B' is constant".
Given system equations:
4x + 3y = 10 (equation 1)
-6x - 5y = -16
⇒ (6x + 5y) = 16 (equation 2)
Option. 1: - 12x - 9y = - 30
⇒ - 3(4x + 3y) = - 3
⇒ (4x + 3y) = 10 (equation 3)
Again, 12x + 10y = 32
⇒ 2(6x + 5y) = 16
⇒ (6x + 5y) = 16 (equation 4)
Option. 2: 20x + 15y = 50
⇒ 5(4x + 3y) = 50
⇒ (4x + 3y) = 10 (equation 5)
Again, -18x -15y = -48
⇒ - 3(6x + 5y) = - 48
⇒ (6x + 5y) = 16 (equation 6)
Option. 3: 24x + 18y = 60
⇒ 6(4x + 3y) = 60
⇒ (4x + 3y) = 10 (equation 7)
-24x - 20y = -64
⇒ - 4(6x + 5y) = - 64
⇒ (6x + 5y) = 16 (equation 8)
Option. 4: 40x + 30y = 100
⇒ 10(4x + 3y) = 100
⇒ (4x + 3y) = 10 (equation 9)
Again, 36x + 30y = -96
⇒ 6(6x + 5y) = -96
⇒ (6x + 5y) = -16 (equation 10)
Therefore, except for the option(4), all system of equations have same solution.
Learn more about a linear equation here: https://brainly.com/question/13997560
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