Which statements are true regarding the system of equations?check all that apply
2 answers:
<h2>Answer:</h2>
The statements which are true regarding the system of equations is:
- The lines are parallel.
- The slopes are equal.
- The y-intercepts are different.
- The system has no solution.
The equation of a line in slope-intercept form is given by:
where m is the slope of the line and c is the y-intercept of a line.
The first equation is:
i.e. on converting this equation to slope-intercept form we get:
i.e.
The slope of first line is: -0.8
and y-intercept is: 3
and the second equation is:
i.e. on converting this equation to slope-intercept form we get:
The slope of second line is: -0.8
and y-intercept is: 4
Since, the slope of both the line are equal (i.e. -0.8)
This means that the two lines are parallel and hence they will never coincide.
Hence, the system has no solution.
Also, the y-intercepts are different.
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The order will be IV, III, I, and II.
<h2>Polynomial</h2>Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Given
I. x + 2xyz
II. 9x³y²
III. 18x² + 5ab - 6y
IV. 4 + 3x² - x - 4
The polynomial expressions from least to greatest are based on their degree.
<h3>How to organize?</h3>4 + 3x² - x - 4 is a biquadratic ploynolmial.
18x² + 5ab - 6y is a cubic polynomial.
x + 2xyz is a quadratic polynomial.
9x³y² is a monomial polynomial.
So the order will be IV, III, I, and II.
More about the polynomial link is given below.