Question

Choose the equation that combines with the following equation to create a system of linear equations with infinitely many solutions? 113x=53y−2

Answer 1

I can't see a list but any equation which is a multiple of the given equation would do.

For example we could multiply each term in the equation by 2 to give:-

226x = 106y - 4.

Answer 2

B.
`22x=10y-12`

D.
`11x=5y-6`

Explanation:

We are given that an equation

`(11)/(3)x=(5)/(3)y-2`

We have to find the equation that combines with the given equation to create a system of linear equations with infinitely many solutions.

Condition of infinitely many solutions:

`a_1x+b_1y+c_1=0`

`a_2x+b_2y+c_2=0`

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

A.
`33x=15y-16`

`(11)/(3)x-(5)/(3)y+2=0`

`33x-15y+16=0`

`a_1=(11)/(3),b_1=-(5)/(3),c_1=2`

`a_2=33,b_2=-15,c_2=16`

`(a_1)/(a_2)=((11)/(3))/(33)=(1)/(9)`

`(b_1)/(b_2)=(-(5)/(3))/(-15)=(1)/(9)`

`(c_1)/(c_2)=(2)/(16)=(1)/(8)`

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

Hence, it is false.

B.
`22x=10y-12`

`22x-10y+12=0`

`(a_1)/(a_2)=((11)/(3))/(22)=(1)/(6)`

`(b_1)/(b_2)=(-(5)/(3))/(-10)=(1)/(6)`

`(c_1)/(c_2)=(2)/(12)=(1)/(6)`

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

Hence, it is true.

C.
`10x=4y-5`

`10x-4y+5=0`

`((11)/(3))/(10)=(11)/(30)`

`(-(5)/(3))/(-4)=(5)/(12)`

`(11)/(130)\\eq(5)/(12)`

`(a_1)/(a_2)\\eq (b_1)/(b_2)`

Hence, it is not true.

D.
`11x=5y-6`

`11x-5y+6=0`

`((11)/(3))/(11)=(1)/(3)`

`(-(5)/(3))/(-5)=(1)/(3)`

`(2)/(6)=(1)/(3)`

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

Hence, it is true.