A Find values of the s which guarantee this equation will ha

A): Find values of the *\'s which guarantee this equation will have a solution. How many ways can this be done?

In what ways can you choose the *\'s to fuarantee that the equaiton will not a solution?

THREE VIEWPOINTS ASSESSMENT 1 Task 3. Consider the equation below: 2 5 A): Find values of the x\'s which guarantee this equation will have a solution. How many ways can this be done?

Solution

First we solve the two linear equations given by first two rows

3x+7y=1

2x+5y=1

SOlving gives

x=-2,y=1

To find *s that guarantee a solution the *s must give an equation which is linear combination of first two equations is

a(3x+7y-1)+b(2x+5y-1)=0

(3a+2b)x+(7a+5b)y=a+b

We need a+b=0

Hence, a=-b

So,

(3a+2b)x+(7a+5b)y=ax+2ay= a(x+2y) for any a

This can be done in infinitely many ways

B)

Any equation not of the form:*s chosen so that not of the form

a, 2a will guarantee no soluton.