Question

40 points!! need help asap

1. 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

2. how many solutions does the system of equations have?
[y = 4x + 3 and 2y - 8x = 3]

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

3. 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

4. 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

Answer 1

#1.

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

One answer

#2.

Here, y = 4x + 3

y - 4x = 3

Multiply by 2,

2y - 8x = 6

Compare with second equation,

6 ≠ 3

In short, System of Equation does not have any solution. [ Option D ]

#3.

2y=6

3x-6y=18

Divide first equation by 2: y=3

Substitute y=3 into second equation: 3x-6(3)=18

Solve for x: 3x=36 x=12

Therefore there is only one solution: x=12 y=3

#4.

y - 7x = -14

7y - 49x = -2

Rewrite the first equation as "y =" so that it can be substituted into the second equation and solve for x.

y = 7x - 14

7(7x - 14) - 49x = -2

49x - 98 - 49x = -2

-98 = -2

Since the variables cancel and the equation is not true there is no solution.

The lines are parallel and will not intersect.