Math Help Please?

Question

i know for most of you it is easy but for me it is hard please show work and i will give 10 pts

4. Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-7x + y = 4
2x + 8y = 0



5. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
x + y = 4
2x – y = 2



6. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
5x – 3y = 3
-10x + 6y = -4

Answer 1

4. -7x + y = 4
2x + 8y = 0

Rewrite as y = 4 + 7x, now put into second equation:
2x + 8(4 + 7x) = 0
2x + 32 + 56x = 0
58x = -32
x = -16/29 giving y = 4 + 7(-16/29) = 4/29
(-16/29, 4/29)


5.
x + y = 4
2x – y = 2

Add the top to bottom equation
3x = 6
x = 2
Now put x = 2 into top equation, y = 4-2 = 2
(2,2)



6. 5x – 3y = 3
-10x + 6y = -4
2 times top equation + bottom equation
10x -6y = 6
-10x + 6y = -4

0 = -2 ??

In this case, there is no solution as the 2 lines do not intersect each other.
Rewriting:
5x – 3y = 3 so -10x + 6y = -6
-10x + 6y = -4

These 2 lines are parallel, so they do not intersect, so no solution

Answer 2

i) -7x + y = 4
ii) 2x + 8y = 0

in i), add 7x to both sides (to isolate y)
y = 7x + 4
pluginto ii)
2x + 8(7x+4) = 0
combine and simplify
2x + 56x + 32 = 0
58x = -32
x = -32/58 = -16/29
y = 7x + 4 = 7(-16/29) + 4 = -112/29 + 116/29 = 4/29
(-16/29, 4/29)

x + y = 4
2x-y = 2

add the two equations to eliminate y.. 3x = 6. x = 2. 2 + y = 4. y = 2
(2, 2).


5x - 3y = 3
-10x + 6y = -4

multiply the first equation by 2 (to get like but opposite signed coefficients of y) and then add the second equation.

10x - 6y = 6.
-10x + 6y = -4.

adding, 0 = 2. whoops. No solution.

Answer 3

4) -7x+y=4, solve for y>> +7x to both sides, y= 7x+4
2x+8y=0, now sub y into second equation 2x+8(7x+4)=0
2x+56x+32=0, 58x= -32, divide by 58 and reduce x= -16/19. Plug that into the first equation y=7(-16/19)+4 and reduce to y= -36/19. Your coordinates are (-16/19, -36/19).

5) x+y=4
2x-y=2
Since you have a +y and a - y just add all like terms giving you 3x=6, divide by 3 and you get x=2, plug 2 in for x in the first problem (2)+y=4, y=2, (2,2) is your solution.

6)5x-3y=3
-10x+6y=4
Multiply the top prob by 2 ( all terms ) giving you
-10x+6y=4
10x-6y=6 }add all terms
0x+0y= 10, since there are no 0x and 0y we have no solution as our answer.
Hope this helps!!!

Answer 4

4. substitution method.

1 -7x+y=4
2 2x+8y=0

take one equasion and solve for x or y. I will take equasion 1.
-7x+y=4 move the -7x over so you have y=
y=7x+4 now you plug this into equasion 2.

2. 2x+ 8(7x+4)=0
2x + 56x + 32=0
58x + 32 = 0 move the 32 over
58x = -32
x= -16/29 now you have your x cordinate now plug x in either origional equasion and get your y cordinate I will use equasione 1.
-7(16/29) + y = 4
3 25/29 + y = 4
y= 4-3 25/29
y=4/29 (-16/29 , 4/29)

independant

5.elimination method or (addition method)

this particular problem is already partially done for you.
1. x+y=4
2. 2x+8y=0
-----------------
3x =0 x=0 now plut x coordinate to one of the equasions 1 I say would be the easiest.
y=4 (0,4) also independent


5.) with your last equasion using the elimination method comes out to o=2 which is no solution
both x and y coordinate cancel out

Answer 5

4. Solve the first equation for "y":

y=7x+4...substitute in equation 2:

2x + 8(7x+4) = 0
2x+56x+32 = 0
58x+32=0
58x=-32
x = -32/58 = -16/29

Solve for y:

-7(-16/29) + y = 4
112/29 + y = 4
y=4-112/29 = 116/29-112/29 = 4/29

(-16/29, 4/29)


5. x + y = 4
2x - y = 2
----------------
3x = 6
x=2
Solve for y: 2+y=4....y=2

(2,2)

6. 5x - 3y = 3
-10x + 6y = -4

Multiply row 1 by "2":

10x - 6y = 6
-10x +6y = -4
-------------------------
0 +0 = 2
0 = 2
FALSE....no solution