Question

Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.

y = –2x + 4

6x + 3y =

–12
–4
0
4
12

Answer 1

-12, -4,0, 4

Explanation:

`y=-2x+4`

`6x+3y= ?`

We need to find out the unknown number

When the system of equations have no solution only the lines are parallel.

the lines are parallel then the slopes are equal and y intercept are different

`y=-2x+4`, slope is the coefficient of x. slope = -2

`6x+3y= a`

Move 6x to the other side and Solve the equation for y

`3y= -6x+a`, divide both sides by 3

`y=-2x+ (a)/(3)`. slopes are same . y intercept can be any number.

`(a)/(3)` not equal to 4

So the value of 'a' not equal to 12

Hence y intercept are all numbers except 12

Answer 2

In order for the system of equations to have no solutions, the equations must be equivalent.
The answer can be solved by trial and error or by changing the second equation to the slope-intercept form and comparing it with the first equation.
If we let
6x + 3y = a
Then, the slope intercept form is:
y = -2x + a/3

Comparing the two equations, we equate the constant term:
a/3 = 4
a = 12