Math Help???

Question

Solve and check the following systems by graphing. Show steps. Write equations and points plotted on graph

1.(x – y = 2 )
(x + y = -4)


2.(x + 3y = 6)
(x + 3y = -3)


3.( y = -2x)
(y – 3x = 0 )

For each of the following problems, (a) choose a variable and indicate what it represents, (b) set up a system of equations to represent the problem described, (c) solve the equations

10.Find two numbers whose sum is 131 such that one number is 5 less than three times the other number.

11.Cynthia has 30 coins, consisting of dimes and quarters that total $5.10. How many coins of each kind does she have?

I have no idea how to do this. THANKS FOR ANY HELP!!!

Answer 1

10. Let the unknown numbers be a and b

(1) a + b = 131
(2) a = 3b - 5

Substitute the value of a from (2) into (1) gives:

3b - 5 + b = 131
4b - 5 = 131
4b = 136
b = 34

substitute the value of b back into (1) gives:

a + 34 = 131
a = 97

Thus the two numbers are 34 and 97

11. Let q be the number of quarters and d the number of dimes

(1) q + d = 30

(2) 25q + 10d = 510
which simplifies to: 5q + 2d = 102

From (1) q = 30 - d

Substitute q into (2) gives

5 * (30 - d) + 2d = 102
150 - 5d + 2d = 102
3d = 48
d = 16

Substitute d back into (1) gives

q + 16 = 30
q = 14

Therefore there are 14 quarters and 16 dimes

Answer 2

You need to draw the graphs.

But 1. add gives 2x = -2 => x = -1, y = -3
2. no solution - the two lines are parallel and never meet
3. y = -2x and y = -3x only meet at (0,0)

10. first number = n
second number = m
n + m = 131
n + 5 = 3m = 3 (131 - n) = 393 - 3n
4n = 388; n = 97, m = 34

11. nos of each type - a, b
a + b = 30
10a + 25b = 510 = 10a + 25(30 - a) = 10a + 750 -25a

15 a = 240; a = 16, b = 14

16 dimes, 14 quarters