Please help with these elimination problems?

Question

Please could you help me with this? and show me how you got th answers too,?
I do know that you have to plug in the variable for the value for one (x or y ).
Use elimination to solve each system of equations.

5.) 3x-4y=6
2x+3y=3

6.) 3x-5y=1
2x+3y= -12
use substitution or elimination to solve these system of equations-

7.) x+y=13
2x-3y=1

8.) 9x+2y=5
3x-y= -10

9.) 2x+y=1
x=5+y

10.) x= -8y
2x-3y=1

11.) 2x+4y=12
-3x+3y=63

12.) 5x-2y= -1
3x-y= -2

13.) Bill leaves his house for Ashley's house riding his bicycle at 8 miles per hour. At the same time, Ashley leaves her house heading toward Bill's house at 3 miles per hour.

a.) write a system of equations to represent the distance, d, each is from Ashley's house in h hours. They live 8.25 miles apart.

b.) Solve the system to determine how long they travel before meeting.

Answer 1

5.)
equation 1: 3x-4y=6 (multiply this by -2)
equation 2: 2x+3y=3 (multiply this by 3)
new equation 1: -6x + 8y = -12
new equation 2: 6x + 9y = 9
Add the two equations
17y = -3
y = -3/17
Put y back into equation 1
3x - 4(-3/17) = 6
3x +12/17 = 6
3x = 90/17
x = 30/17

6.)
Equation 1: 3x-5y=1 (multiply by 2)
Equation 2: 2x+3y= -12 (multiply by -3)
New Eq 1: 6x - 10y = 2
New Eq 2: -6x - 9y = 36
Add the two equations
-19y = 38
y = -2
substitute for y in equation 1
3x -5(-2) = 1
3x + 10 = 1
x = -3

7.)
x+y=13; so x = 13-y
2x-3y=1
substitute in the second equation
2(13-y) -3y = 1
26 - 2y - 3y = 1
-5y = - 25
y = 5
substitute for y in the first equation
x + 5 = 13
x = 8

8.) 9x+2y=5
3x-y= -10; so y = 3x + 10
substitue in eq 1
9x + 2(3x+10) = 5
15x = -15
x = -1
substitute for x in equation 1
9*(-1) + 2y = 5
-9 + 2y = 5
2y = 14
y = 7

9.) 2x+y=1
x=5+y (use this and substitute in eq 1)
2(5+y) + y = 1
10 + 3y = 1
3y = -9
y = -3
2x -3 = 1
2x = 4
x = 2

10.) x= -8y (use this in the second eq)
2x-3y=1
2(-8y) - 3y = 1
-16y - 3y = 1
y = -1/19
x = -8(-1/19) = 8/19

11.) 2x+4y=12; This is the same as x + 2y = 6
-3x+3y=63; this is the same as -x + y = 21
Add the two equations
3y = 27
y = 9
2x + 4*9 = 12
2x = 12 - 36 = - 24
x = -12

12.) 5x-2y= -1
3x-y= -2; this is the same as 3x + 2 = y
substitute in eq 1
5x - 2(3x+2) = -1
-x -4 = -1
-3 = x
3(-3) - y = -2
-9 -y = -2
y = -7

13a) In H hours, Ashley is 3H from her house D= 3H
In H hours, Bill is 8.25 - 8H from her house D = 8.25 - 8H
3H = 8.25 - 8H
11H = 8.25
H = .75 hr = 45 minutes

Notice that you don't need algebra to solve this puzzle. They are 8.25 miles apart and are coming toward each other at the rate of 11 mph. 8.25/11 = .75

Answer 2

You have to add the like terms