Vineet solved a system of equations by substitution. in his work, he substituted an expression for one of the variables and solved for the value of the other. this resulted in the equation 7 = 9. what can vineet conclude? (a)the solution to the system is (7, 9). (b)the system of equations does not have a solution. (c)the work must be incorrect because it is not possible to get this equation. (d)the system of equations has infinitely many solutions.

Answer b: the system of equations does not have a solution

Suppose the systems consits of two first grade equations with two varaibles. If the two equations are parallel you would obtaing a result like Vinnet.

This is an example:

x = y + 1

7x = 7y +  9

substitue to get:

7(y+1) = 7y +9
7y + 7 = 7y + 9
7=9

There is not mistake, the system has no solutions, because the two equations represent parallel lines, which do no intercept one to each other.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

6hope this ! ! ’