Question

1. determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

$-5x + 3y = -9$
$-20x + 11y = -48$
a. one solution
b. infinitely many solutions
c. no solutions

Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by 4:
$$4(-5x + 3y) = 4(-9) \implies -20x + 12y = -36$$

Step2: Subtract second equation

Subtract $-20x + 11y = -48$ from the new equation:
$$(-20x + 12y) - (-20x + 11y) = -36 - (-48)$$
$$y = 12$$

Step3: Solve for $x$

Substitute $y=12$ into $-5x + 3y = -9$:
$$-5x + 3(12) = -9$$
$$-5x + 36 = -9$$
$$-5x = -45$$
$$x = 9$$

Answer:

A. One Solution