Margaret ran 2 more miles than lynn. the sum of their distance is 20 miles. (a) define your variables. (b) write algebraic expressions for the distance each person ran. (c) write an equation that can you solve the problem. (d) how far did margaret run? (e) how far did lynn run?me solve all a-e : b

It is given in the question that

Margaret ran 2 more miles than Lynn. The sum of their distance is 20 miles.

a. Let Lynn runs x miles and Margaret runs y miles .

And them sum of their distances is 20 miles. That is

And it is given that Margaret runs 2 more miles than Lynn .

Therefore,we have

b. Algebraic expressions of the distances each person ran

c. So the equations are

Substituting the value of y in first equation

e. THerefore Lynn run 9 miles.

d. Margreta run

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions