Question

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

y = -2x + 4

6x + 3y =

Answer 1

12

Explanation:

We are given that two equations

`y=-2x+4`

`6x+3y=`

We have to find the value in the blank space when we place that value then system of equations have infinitely many solutions

Equation I can be written as

`2x+y-4=0`

Let a be the value that placed in blank space and system have infinitely many solutions

Then
`6x+3y-a=0`

We know that condition of infinite solutions

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

Substitute the values then we get

`(2)/(6)=(-4)/(-a)`

`(1)/(3)=(4)/(a)`

`a=4* 3`

a=12

Hence, when we placed 12 in the box then system of equations would have infinitely many solutions .

'

Answer 2

The missing value is 12

Explanation:

we know that

If the system of equations has infinitely solutions , then the two equations must be the same

so

`y=-2x+4` ---->
`2x+y=4` -----> equation A

Multiply equation A by 3 both sides

`3*(2x+y)=4*3`

`6x+3y=12` ----> equation B

`6x+3y=?` -----> equation C

equate equation B and equation C

The missing value is 12