Question 1190891: The solution to this system of equations is (-2, 3). Find the values of p and q. [4]
px+qy=13
qx+(p+1)y=1
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equations are:
px + qy = 13
qx + (p+1)y = 1
the solution is (-2,3).
that means that x = -2 and y = 3.
replace x and y with these values in the equation to get:
-2 * p + 3 * q = 13
-2 * q + 3 * (p + 1) = 1
simplify the second equation to get:
-2 * q + 3 * p + 3 = 1
subtract 3 from both sides to get:
-2 * q + 3 * p = -2
rearrange the terms to get:
3 * p - 2 * q = -2
your two equations are now:
-2 * p + 3 * q = 13
3 * p - 2 * q = -2
multiply both sides of the firest equation by 3 and multiply both sides of the second equation by 2 to get:
-6 * p + 9 * q = 39
6 * p - 4 * q = -4
add the two equations together to get:
5 * q = 35
solve for q to get:
q = 7
replace q with 7 in the first equation to get:
-6 * p + 9 * 7 = 39
simplify to get:
-6 * p + 63 = 39
subtract 63 from both sides to get:
-6 * p = -24
divide both sides by -6 to get:
p = 4
your values for p and q are now:
p = 4
q = 7
go back to the two equations of:
-2 * p + 3 * q = 13
-2 * q + 3 * (p + 1) = 1
replace p with 4 and q with 7 to get:
-2 * 4 + 3 * 7 = 13 becomes -8 + 21 = 13 which becomes 13 = 13.
-2 * 7 + 3 * (4 + 1) becomes -14 + 15 = 1 which becomes 1 = 1.
this confirms the values of p and q are correct.
your solution is that the values of p and q are 4 and 7, respectively.
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