Ben rents a car for one day. The charge is $20 plus the $0.12 per mile. He wants to
2 answers:
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Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
second equation:
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Answer:
Step-by-step explanation:
Let the number be x;
The product of 4 and the number will be;
The the square of the number is given as;
Taking the difference of both expressions above;
Factor out the common term:
Hence the difference between the product of 4 and a number and the square of the number is