Answer:
The intersections of the graphs of an equation system correspond to the system's solutions. A linear-quadratic system can have zero, one, or two solutions because a line can intersect a parabola zero, one, or two times.
Step-by-step explanation:
The statement "a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions" is true .
A linear equation is an algebraic equation of the form [tex]y= mx+b.[/tex]involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
We define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is , [tex]y = ax^2 + bx + c[/tex]
where a, b, and c are numbers and a cannot be 0.
According to the question
A system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions.
This statement is true as
if we see graphically
A quadratic equation is a parabola and a linear equation is a straight line.
There could be 3 situations of intersection of line and parabola
1. straight line never crosses the parabola
i.e line passing above or below parabola without touching
it is called zero solution
2. where the straight line is a tangent to the parabola, 'touching' it at only one point.
i.e single point lies in both line and parabola
it is called one solution
3. the line cuts across the parabola, it will cut the parabola at 2 points
it is called two solution .
Hence, The statement " a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions "is true .
To know more about linear equation and quadratic equation here:
https://brainly.com/question/2263981
#SPJ2
