Question 27272: Determine whether the given ordered pair is a solution of the system of equations.
1.(3,2);2x+3y=12
x-4y= -5
2.(1,5);5x-2y=-5
3x-7y=-32
3.(3,2);3t-2s=0
t+2s=15
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! Determine whether the given ordered pair is a solution of the system of equations.
1 2x+3y=12 ----(1)
x-4y= -5 ----(2)
To check if the ordered pair (3,2) is a solution of the given system
put x = 3 and y = 2 in (1) as well as in (2) and check if the equations satisfy these values that is check if LHS of (1) = RHS of (1) for these values and similarly check if LHS of (2) = RHS of (2) for these values
x= 3 and y = 2 in (1)
LHS = 2x + 3y
= 2 X 3 + 3 X 2 = 6 + 6 = 12 = RHS
x= 3 and y = 2 in (2)
LHS = x - 4y
= 3 - 4 X 2 = 3 - 8 = -5 = RHS
As the two given equations hold for x = 3 and y = 2 we conclude that the ordered pair (3,2) is a solution of the given system of equations.
2.(1,5);5x-2y=-5
3x-7y=-32
5x-2y=-5 ----(1)
3x-7y=-32 ----(2)
x = 1, y = 5 in (1) implies
LHS = 5x - 2y = 5 X 1 - 2 X 5 = 5 - 10 = -5 RHS
x = 1, y = 5 in (2) implies
LHS = 3x - 7y = 3 X 1 - 7 X 5 = 3 - 35 = -32 = RHS
As the two given equations hold for x = 1 and y = 5 we conclude that the ordered pair (1,5) is a solution of the given system of equations.
3.(3,2);3t-2s=0
t+2s=15
Put t = 3 and s = 2 in both the equations and try as above
3t - 2s = 0 ----(1)
t + 2s = 15 ----(2)
t = 3, s = 2 in (1) implies
LHS = 3t - 2s = 3 X 3 - 2 X 2 = 9 - 4 = 5 not equal to RHS
This implies the ordered pair (3,2) is NOT a solution of the given system of equations.
Note: You will have to verify for the second equation only when the values hold in the first equation
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