Answer:
[tex]p =2.5[/tex]
[tex]q = 0.5[/tex]
Step-by-step explanation:
Given
[tex]2x + 3y = 7[/tex]
[tex]( p-q ) x + (p+q) y = 3 p + q -2[/tex]
Required
Find p and q
To do this, we make direct comparison between the given expressions.
[tex]2x + 3y = 7[/tex] and [tex]( p-q ) x + (p+q) y = 3 p + q -2[/tex]
This implies that:
[tex](p - q)x = 2x[/tex]
[tex](p+q)y = 3y[/tex]
[tex]3(p + q) - 2 = 7[/tex]
So, we have:
[tex]p - q = 2[/tex] --- (1)
[tex]p+q =3[/tex] -- (2)
[tex]3(p + q) - 2 = 7[/tex] --- (3)
If [tex](1)\ and\ (2)[/tex] are true, then [tex](3)\ must[/tex] be true.
So, we only solve [tex](1)\ and\ (2)[/tex]
Add (1) and (2) to eliminate q
[tex]p+p-q+q=2+3[/tex]
[tex]2p=5[/tex]
Solve for p
[tex]p = 5/2[/tex]
[tex]p =2.5[/tex]
Substitute [tex]p =2.5[/tex] in (2)
[tex]p+q =3[/tex]
[tex]q = 3 - p[/tex]
[tex]q = 3 - 2.5[/tex]
[tex]q = 0.5[/tex]
