B) exactly two solution
C) infinite solutions
D) exactly one solution
A system of linear equation can have no solutions , many solutions or exactly one solution .
Let's check out example of each.
So all of these describes a system of linear equations except two solutions.
So the correct option is B
In a system of linear equations, the lines represented by the equations can either intersect at a single point, don't intersect at all, or coincide entirely. However, they can't intersect at exactly two different points. Hence, the system of linear equations cannot have 'Exactly two solutions'.
In mathematics, specifically in the study of linear equations, there are various possibilities for the number of solutions a system of linear equations can have. These include having no solution (when the lines are parallel and never intersect), exactly one solution (when the lines intersect at one point), or infinite solutions (when the two lines coincide).
Among the provided options, the one that cannot describe a system of linear equations is 'Exactly two solutions'. A system of linear equations cannot have exactly two solutions. It is because the lines representing the equations can either intersect at a single point, don't intersect at all, or coincide, mimicking each other entirely. But it is impossible for them to intersect at exactly two different points.
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a. 1.5
b. 9
c. 3
d. 4
Answer:
Its 3
Step-by-step explanation:
The product of the given equation [(x + 1)(x - 1)]2 can be mentally calculated by recognizing it as a difference of squares expression followed by applying the square of a binomial formula, giving us x^4 - 2x^2 + 1 as the final answer.
To find the product of the given equation mentally, we need to understand some basic algebraic laws. (x + 1)(x - 1) is a difference of squares, which simplifies to x2 - 1. We then square this expression, as indicated by the '2' outside the parentheses, which gives us (x2 - 1)2.
Finally, applying the square of a binomial formula (a - b)2 = a2 - 2ab+ b2 on our expression, we get x4 - 2x2 + 1 as the final product. Now this final product is the simplest form of your given equation.
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