Question

Student Produced Response - Calculator

11
ax+by=10
3x + 4y = 20
In the system of equations above, a and b are
constants. If the system has infinitely many
solutions, what is the value of a/b?​

Answer 1

`(a)/(b)=0.75`.

Explanation:

If two equations
`a_1x+b_1y+c_1=0` and
`a_2x+b_2y+c_2=0` has infinitely many solutions, then

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

The given equations are

`ax+by=10`

`3x+4y=20`

It is given that the above system of equations has infinitely many solutions. So,

`(a)/(3)=(b)/(4)=(10)/(20)`

`(a)/(3)=(b)/(4)=(1)/(2)`

Now,

`(a)/(3)=(1)/(2)` and
`(b)/(4)=(1)/(2)`

`a=(3)/(2)` and
`b=(4)/(2)`

`a=1.5` and
`b=2`

So, a=1.5 and b=2.

Now,

`(a)/(b)=(1.5)/(2)=0.75`

Therefore,
`(a)/(b)=0.75`.