A system of equations consisting of a linear equation and a quadratic equation ____ has two solutions.
a. always
b. sometimes
c. never **
The solutions given by the quadratic formula are ____ integers.
a. always
b. sometimes **
c. never
Can someone check this?
# 1
Never
#2
Sometimes
#1 nope
consider as you graph
y=x^2, y=x+1
y=x^2, y=x-1
#2 correct
Sure, I can check this for you. In the first question, a system of equations consisting of a linear equation and a quadratic equation sometimes has two solutions. So, the correct answer is b. sometimes.
In the second question, the solutions given by the quadratic formula are sometimes integers. It depends on the specific values of the coefficients in the quadratic equation. So, the correct answer is also b. sometimes.
I hope that helps! Let me know if you have any more questions.
To determine if a system of equations consisting of a linear equation and a quadratic equation has two solutions, we need to consider the possibilities.
In general, a linear equation represents a straight line, and a quadratic equation represents a curve. When we solve a system of linear and quadratic equations, the number of solutions depends on the intersection of the line and the curve.
1. If the line and the quadratic curve intersect at two distinct points, then the system of equations has two solutions. In this case, option "b. sometimes" would be correct for the first question.
2. If the line is tangent to the quadratic curve at one point, then the system of equations has one solution. In this case, option "c. never" would be correct for the first question.
3. If the line and the quadratic curve do not intersect, then the system of equations has no solution. In this case, option "c. never" would be correct for the first question.
Regarding the second question, the solutions given by the quadratic formula can be classified in three scenarios:
1. If the discriminant (the term inside the square root in the quadratic formula) is a perfect square, then the solutions will be rational integers. In this case, option "a. always" would be correct.
2. If the discriminant is not a perfect square but still a rational number, then the solutions will be rational numbers but not necessarily integer values. In this case, option "b. sometimes" would be correct.
3. If the discriminant is an irrational number, then the solutions will also be irrational numbers. In this case, option "b. sometimes" would be correct.
In summary, the correct answer for the first question is option "b. sometimes," and the correct answer for the second question is also option "b. sometimes."
Q: A system of equations consisting of a linear and a quadratic equation______ has one solution.
A: Sometimes
Q: The solutions given by the quadratic formula are ______ irrational.
A: Sometimes