Question

How many solutions?
y = -8x + 5 and 24x + 3y = -8

A. one
B. infinitely many
C. no solutions

Answer 1

Given :- How many solutions ?

y = -8x + 5 and 24x + 3y = -8

A. one

B. infinitely many

C. no solutions

Answer :-:

→ y = -8x + 5

→ y + 8x = 5

→ 8x + y = 5 ---------- Equation (1)

now,

→ 24x + 3y = (-8) --------- Equation (2)

multiplying Equation (1) by 3 we get,

→ 3(8x + y) = 5*3

→ 24x + 3y = 15

putting value of Equation (2) now, we get,

→ (-8) = 15

which is not possible.

therefore, we can conclude that, the given equations have no solution . (Option C) (Ans.)

Learn more :-

Suive.

4) Divide 20x5 ÷ 4x2

https://brainly.in/question/38299916

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The number of solutions of

y = - 8x + 5 and 24x + 3y = - 8

A. one

B. infinitely many

C. no solutions

CONCEPT TO BE IMPLEMENTED

A pair of Straight Lines

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: \: and \: \: \: a_2x+b_2y+c_2=0}$

is said to have no solution if

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

EVALUATION

Here the given pair of lines are

y = - 8x + 5 and 24x + 3y = - 8

Which can be rewritten as

8x + y - 5 = 0 - - - - - - (1)

24x + 3y + 8 = 0 - - - - - (2)

Comparing with the lines

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

We have

$\displaystyle \sf{ a_1 = 8 \: , \: b_1 = 1 , c_1= - 5 \: and \: \: a_2 = 24 \: , \: b_2 = 3\: , \: \: c_2= 8}$

Now

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{8}{24} \ = \: \frac{1}{8}}$

$\displaystyle \sf{ \: \frac{b_1}{b_2} = \frac{1}{ 3} }$

$\displaystyle \sf{ \frac{c_1}{c_2} = \frac{ - 5}{8} }$

$\displaystyle \sf{ \therefore \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

So the given lines have no solution

FINAL ANSWER

Hence the correct option is C. no solutions

GRAPHICAL METHOD

Here the given pair of lines are y = - 8x + 5 and 24x + 3y = - 8

Which can be rewritten as

8x + y - 5 = 0 - - - - - - (1)

24x + 3y + 8 = 0 - - - - - (2)

We now plot them and get the lines

Red line : 8x + y - 5 = 0

Green line : 24x + 3y + 8 = 0

We see that given Lines are parallel

We know that for a given pair of parallel lines there is solution

FINAL ANSWER

Hence the correct option is C. no solutions

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. 2x+3y=12 and 4x+5y=22

https://brainly.in/question/18427922

2. Two straight lines have equations

y=px+4 and py=qx−7, where p and q are constants. The two lines meet at the point (3,1...

https://brainly.in/question/34443315