Question

px + 3y = 2(1 - y) + 1
5 + y = 3(1 + y) + 2x
In the system of linear equations above, p is a constant. For what value of p does the equation have exactly one solution (x, y) with y = 2?

• A. -1/7
• B. 7
• C. -11
• D. 11/7

Answer 1

The correct option is B 7

Consider the equations
px + 3y = 2(1 - y) + 1 ...... (1)
5 + y = 3(1 + y) + 2x ....... (2)
Given: y = 2
Substitute value in equation (2), to find the value of x.
5 + 2 = 3(1 + 2) + 2x
7 = 3 \times 3 + 2x
7 = 9 + 2x
Subtracting 9 on both sides
7 - 9 = 9 - 9 + 2x
-2 = 2x
X = -1
Now, that we have value of both x and y, use the value in the first equation, to find the value of p.
P(-1) + 3(2) = 2(1 - 2) + 1
-p + 6 = -1
-p = - 7
p = 7
Therefore, the answer is 7.