Which values of p and q result in an equation with exactly one solution? px-43=-42x+q choose all answers that apply: a) p=-43 and q=-43 b) p=42 and q=43 c) p=43 and q=−42 d) p=42 and q=42

P = -19, Q = 18

Step-by-step explanation:

Px + Q = -19x + 18

Px = -19x                Q = 18

÷x     ÷x      

P   = -19

All are valid

Step-by-step explanation:

Px - 43 = -42x + Q (rearrange)

x = (Q+43) / (P + 42)  <Substitute options for P & Q into this equation to see which combination gives exactly 1 solution for x

A) P=42, Q = 42; x = (42+43) / (42+42) = 1.011 (only 1 solution = valid)

B) P=43, Q = -42; x = (-42+43) / (43+42) = 0.012 (only 1 solution = valid)

C) P=-43, Q = -43; x = (-43+43) / (-43+42) = 0 (only 1 solution = valid)

D) P=42, Q = 43; x = (42+43) / (42+42) = 1.023 (only 1 solution = valid)

C. Q=−31, P = -2

Step-by-step explanation:

2x+Q = Px−31

A. Q = −2 and P=2

2x+Q=Px−31

2x - 2 =2x - 31

0x = -29

0 ≠ -29 : NO SOLUTION

B.Q=31 and P=2

2x+Q=Px−31

2x + 31 = 2x - 31

0x = -62

0 ≠ -62 : NO SOLUTION

C. Q=−31, P = -2

2x+Q=Px−31

2x - 31 = -2x - 31

4x = 0

 x = 0 : ONE SOLUTION

D. Q=-31 and P=2

2x+Q=Px−31

2x - 31 = 2x - 31

0x = 0

0 = 0: Infinitely many solutions

C. Q=−31, P = -2

For any value of P & Q except when both are equal , we get One solution of equation.

Step-by-step explanation:

Given: Linear Equation, Qx - 6 = Px - 103

           This equation has exactly 1 solution.

To find: Value of P and Q

First we solve the linear equation for value of x,

Qx - 6 = Px - 103

Transpose Px to LHS ( Left hand side ) we get,

Qx - Px - 6 = -103

Transpose 6 to RHS ( Right hand side ) we get,

Qx - Px = -103 + 6

Qx - Px = -97

taking x common in LHS, we get

( Q - P )  x =  -97

Traspose ( Q - P ) to RHS, we get

Thus, we are get only 1 value of x but it exist if P ≠ Q

otherwise no solution exist for the given linear Equation.

Therefore, For any value of P & Q except when both are equal , we get One solution of equation.

If P = -42 and Q = -43, the equation has infinitely many solutions.

If P = -42 and Q is not -43, the equation has no solutions.

If P is not equal to -42, the equation will have one solution no matter what the value of Q is.

The left and right parts of this equation represent lines. By setting them equal to each other, you are checking where these lines intersect. Lines intersect in exactly one point only when they have different slopes. So all we do is check the slope of the right side (which is -42) and make sure the slope of the left side (which is P) is not -42. I hope this helps.

brainliest plzz tried really hard on this thx god bless

Its all of the answers in that question

Option A is correct

Values of P = -2 and Q = -31

Step-by-step explanation:

Given the equation:

Now, we put the given values

A.

Q = -31 and P = -2

2x + (-31) = -2x - 31

2x - 31 = -2x -31  

4x = -31 + 31

4x = 0

x = 0    [one solution]

B.

Q = 31 and P = 2

2x + Q = Px -31

2x + 31 = 2x -31

Subtract 2x from both sides we get

31 = -31        False.

C.

Q = -31 and P = 2

2x + (-31) = 2x - 31

2x - 31 = 2x - 31     [More than one solutions, for any x]

D.

Q = -2 and P = 2

2x + Q = Px -31

2x + (-2) = 2x -31

2x -2 = 2x -31

2x - 2x = -31 + 2      

Combine like term;

0 = -29       False.

Therefore, the values of P and Q results in an equation with exactly one solution is; P = -2 and Q = -31

P = 6

Q = 15

How to solve:

Note the equal sign. This means that both expression's out come must equal each other. For that to happen, everything inside both expressions must equal each other. In this case:

6x + Q = Px + 15; 6x + 15 = 6x + 15

hope this helps

p= 58 and q= -78

p= 58 and q= 78

p= −78 and q= −52

are all answers

the answer is c

Step-by-step explanation: