Question

Please Help I need answer fast will mark brainliest
Determine if the system of equations has one solution, no solution or infinitely many solutions. Make sure to show all your work to receive full credit for each question.
-3x-3y=3 y= -5x-17

Show your work by including a written or verbal explanation of WHY your answer includes one solution, no solution or infinitely many solutions

Answer 1

Given Equations :

$=> -3x - 3y = 3 \\ =\bold{-3x - 3y - 3 = 0} ....(i)$

$=> y = -5x - 17 \\ = \bold{5x + y + 17 = 0} ....(ii)$

On Comparing both equations with $\bold{ ax^{2} + bx + c }$, we get

in (i),

$a_1 = -3 \\ b_1 = -3 \\ c_1 = -3$

in (ii),

$a_2 = 5 \\ b_2 = 1 \\ c_2 = 17$

To know it's number of solutions:

we will compare using the following formula:

=> $\frac{a_1}{a_2} ≠ \frac{b_1}{b_2}$ (Lines are intersecting, Only one solution)

=> $\frac{a_1}{a_2} = \frac{b_1}{b_2} ≠ \frac{c_1}{c_2}$ (Lines are parallel, No solutions)

=> $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ (Lines are coinciding, Infinitely many solutions)

On Comparing,

=> $\frac{-3}{5} ≠ \frac{-3}{1} ≠ \frac{-3}{17}$

Hence, Lines are intersecting and they have only one solution.

Answer to the question, 'Why it is the answer ?'

These two equations, when will be drawn on the graph, they will intersect each other. And intersecting lines intersect at only one point. So the solution to both equation will be that point of intersection. Hence, both equation will have only one solution.