# Find the solution to the following   A)p+2q-4=0 7p-q-3=0  by the substitution method.Check answers.Write your solution in the form (x,y),(p,q),or (s,t).

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`1. p +2q - 4=0`  and     `2` .    `7p-q-3=0`

There are 2 unknown variables (p and q) so convert the first equation  `1.`   to the form p= (or q= )

`p+2q -4=0` becomes `p= -2q +4`

and substitute into the other eequation:

`7p-q-3=0` becomes `7(-2q +4) -q -3 =0`

Now simplify:

`therefore -14q+28 -q-3=0`

`therefore -14q-q=3-28`

`therefore -15q=-25`

`therefore q=(-25)/-15`

`therefore q=5/3`

Note that the negative symbols cancel each other out.

Now solve for q by substituting into any one of your previous equations:

`p=-2q+4`

`therefore p= -2(5/3)+4`

`therefore p=-10/3 + 4`

`therefore p = 2/3`

(p;q): (`2/3; 5/3` )

To check substitute both values back into one of the equations. When both sides of the equation equal each other (LHS=RHS) ie left hand side equals right hand side, then the values are correct:

`7p-q-3=0`

`7(2/3) - (5/3) - 3=0`

`14/3 -5/3 - 3 = 0`

`therefore 9/3-3 = 0`

`therefore 3-3=0`

`therefore 0=0`

Therefore LHS=RHS

(p;q);(2/3;  5/3)

Sources:

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`p+2q=4`

`7p - q= 3`

adding the first to the second by 2:

`p+2q+2(7p-q)=p+2q+14p-2q=10`

`15p= 10`    `p=2/3`

from the first row:

`2/3+2q=4`      `2q= 10/3`     `q= 5/3`