Question

PLEASE PLEASE HELP ME!?!?!!?

Determine which system below will produce infinitely many solutions. (2 points)
Select one:
a. 2x + 5y = 24 2x + 5y = 42
b. 3x − 2y = 15 6x + 5y = 11
c. 4x − 3y = 9 −8x + 6y = −18
d. 5x − 3y = 16 −2x + 3y = −7

Answer 1

Ans:- 3rd option

c. 4x − 3y = 9, −8x + 6y = −18

Reason:

For a system of equation to have infinite many solution. At that time,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

In the given equation,
a1 = 4
b1 = -3
c1 = 9
a2 = -8
b2 = 6
c2 = -18

So,
$- \frac{4}{8} = - \frac{3}{6} = - \frac{9}{18} \\ - \frac{1}{2} = - \frac{1}{2} = - \frac{1}{2}$

Hence this equation will have infinite many solution.

Hope this helps!

Answer 2

The system of the equation that produces infinitely many solutions is (4x − 3y = 9) ; (−8x + 6y = −18) and this can be determined by using the condition of having infinitely many solutions.

The system of equation is given below:

$\rm a_1x+b_1y+c_1=0$

$\rm a_2x+b_2y+c_2=0$

For infinitely many solutions the system of the equation must satisfy the below condition:

$\rm \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

Now, check all the given options in order to determine the correct option.

C).

4x − 3y = 9

−8x + 6y = −18

$\dfrac{4}{-8}=\dfrac{-3}{6}=\dfrac{9}{-18}$

Simplify the above expression.

$-\dfrac{1}{2}=-\dfrac{1}{2}=-\dfrac{1}{2}$

Therefore, the correct option is c).

For more information, refer to the link given below:

https://brainly.com/question/900521