Two lines, a and b, are represented by the following equations: line a: y = x − 1 line b: y = −3x + 11 which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point question 4(multiple choice worth 4 points) (08.01) line h is represented by the following equation: 2x + 2y = 8 what is most likely the equation for line k so the set of equations has infinitely many solutions? x + 2y = 2 x + y = 4 2x + y = 6 x − y = 8 question 5(multiple choice worth 4 points) (08.01) line m is represented by the following equation: x − y = 8 which equation completes the system that is satisfied by the solution (18, 10)? 2x − y = 26 x + y = 18 2x − 2y = 36 x − y = −28

Part 1. (3, 2), because both lines pass through this point.

Part 2. x + y = 4

Part 3. 2x − y = 26

Step-by-step explanation:

Part 1.

The given system of equations are

Substitute the value of from one equation to another.

Divide both sides by 4.

The value of x is 3. Put this value in the given equation to find the value of y.

The value of y is 2. Both the equations satisfy by the point (2,3) it means the  both lines pass through this point.

Therefore (3, 2) is the solution, because both lines pass through this point.

Part 2.

The given equation is

The set of equations has infinitely many solutions if both lines coincide each other.

Taking out the common factors.

Divide both sides by 2.

The line is equivalent to . It means both line coincide each other and have  infinitely many solutions.

Therefore the required equation of line is x + y = 4.

Part 3.

The one equation of the system of equations is

The solution of the system of equation is (18,10). It means both the equation are satisfied by the point (18,10).

Put x=18 and y=10 in each option.

Therefore the required equation is 2x-y=26.

the two may have that, even a breakdown is probably offered

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for