Question

Y=3

y = ax+ b
In the system of equations above, a and b are
constants. For which of the following values of a
and b does the system of equations have exactly two
real solutions?
A) a=--2, b=2
B) a= -2, b=4
C) a = 2, b=4
D) a = 4, b=3

Answer 1

The values of a and b that will make the system of equations have exactly two real solutions are a = 3 and b = 0.

Step-by-step explanation:

In order for the system of equations to have exactly two real solutions, the discriminant of the quadratic equation formed by setting the two equations equal to each other should be equal to zero.

The given system of equations is:
y = 3y = ax + b

By simplifying the equations, we get:
y = ax + b

Setting the two equations equal to each other:
y = ax + b

Since the two equations are equal, their coefficients must also be equal:
3 = a
0 = b

Therefore, the values of a and b that satisfy the given conditions are:
a = 3 and b = 0