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3. How many solutions does the system of equations have?

4x = -12y + 16 and x + 3y = 4

a.) one
b.) two
c.) infinitely many
d.) none

4.) How many solutions does the system of equations have?

y = 6x + 2 and y = 6x + 4

a.) one
b.) two
c.) infinite
d.) none

5.) How many solutions does the system of equations have?

x - 2y = 6 and 3x - 6y = 18

a.) one
b.) two
c.) infinitely many
d.) none.

6.) How many solutions does the system of equations have?
y - 7x = -14 and 7y - 49x = -2
a.) one
b.) two
c.) infinitely many
d.) none

I don't know how to do these, and explanation of how these are done would be nice.

Respuesta :

calculista

Answer:

Part 3) Option C infinitely solutions

Part 4) Option D none

Part 5) Option C infinitely solutions

Part 6) Option D none

Step-by-step explanation:

Part 3) we have

[tex]4x=-12y+16[/tex] -----> convert to standard form

[tex]4x+12y=16[/tex] -----> equation A

[tex]x+3y=4[/tex] -----> equation B

Multiply the equation B by [tex]4[/tex]

[tex]4(x+3y)=4*4[/tex] ------> [tex]4x+12y=16[/tex]

The equation A and the equation B are the same

therefore

The system has infinitely solutions

Part 4) we have

[tex]y=6x+2[/tex] ------> equation A

[tex]y=6x+4[/tex] ------> equation B

equation A and equation B are parallel lines, because has the same slope

the slope is equal to [tex]m=6[/tex]

therefore

The system has no solution

Part 5) we have

[tex]x-2y=6[/tex] ------> equation A

[tex]3x-6y=18[/tex] ------> equation B

Multiply the equation A by [tex]3[/tex]

[tex]3(x-2y)=6*3[/tex] -----> [tex]3x-6y=18[/tex]

The equation A and the equation B are the same

therefore

The system has infinitely solutions

Part 6) we have

[tex]y-7x=-14[/tex] ------> equation A

[tex]7y-49x=-2[/tex] ------> equation B

Multiply the equation A by [tex]7[/tex]

[tex]7(y-7x)=-14*7[/tex] -----> [tex]7y-49x=-98[/tex]

Equation A and equation B are parallel lines, because has the same slope

the slope is equal to [tex]m=7[/tex]

therefore

The system has no solution

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