Answer:
[tex]a= 2[/tex]
[tex]b = 3[/tex]
Step-by-step explanation:
Given
[tex]p(x,y) = (6,0)[/tex]
[tex]q(x,y) = (3,2)[/tex]
[tex]ax + by = 12[/tex]
Required
Find a and b
In [tex]p(x,y) = (6,0)[/tex], [tex]x = 6[/tex] and [tex]y = 0.[/tex]
This gives:
[tex]a*6 + b*0 = 12[/tex]
[tex]6a = 12[/tex]
Divide by 6
[tex]a= 2[/tex]
In [tex]q(x,y) = (3,2)[/tex]. [tex]x = 3[/tex] and [tex]y = 2.[/tex]
This gives:
[tex]a*3 + b*2 = 12[/tex]
[tex]3a + 2b = 12[/tex]
Substitute 2 for a
[tex]3*2 + 2b = 12[/tex]
[tex]6 + 2b = 12[/tex]
Collect Like Terms
[tex]2b = 12 - 6[/tex]
[tex]2b = 6[/tex]
Divide by 2
[tex]b = 3[/tex]
