Help with Linear equations in two variables by addition method?

Question

1)

x+5y=7
2x + 7y=8

2)

3x+5y=16
5x-7y=-4

Answer 1

x+5y = 7
2x+7y=8
multiply first by -2
-2x-10y=-14
2x+7y=8
add
-3y = -6
so y = 2
x = 7 - 5y = -3

Answer 2

1) ( x +5y=7 ) x 2
2x+7y=8

2x +10y =14 ---------->equation 1
2x +7y = 8 -----------> equation 2

By adding equations 1 and 2 we get,

2x +10y =14
(-) 2x (-)+ 7y =(-) 8

2x +10y = 14
-2x -7y = -8
3y = 6
y =6/3=2

By substituting y in equation 1 we get,

x + 5(2)=7
x +10=7
x =7 -10= -3

Therefore, x = -3
y = 2

2) (3x +5y =16) x 7
(5x -7y = -4) x 5

15x + 35y = 112----------->equation 1
25x - 35y = -20 ------------>equation 2
40x +0 = 92
x = 92/40
x = 23/10

By substituting x in equation 1 we get,

3 (23/10)+5y =16
69/10 +5y =16
69+50y/10= 16
69 +50y =160
50y = 160-69
50y =91
y = 91/50

Therefore, x = 23/10
y=91/50

Answer 3

for the first question the answer to x=-3 and y=2
by multiplying one of the equations so as to eliminate one of the variables like mulitiplying (x+5y=7) by 2 then the resulting solution is 2x+10y=14
2x+10y=14
- 2x+ 7y =8
___________
0x+ 3y=6
y=2
then substitute y=2 into any one of the two original equations like x+5(2)=7
x+10=7
x=7-10
x=-3
You can try for the second question, the answers are x=2 y=2

Answer 4

1) Multiply the 1st by -2 to get -2x -10y = -14 add to the second now to obtain

-2x +2x -10y +7y =-14 +8 ==> -3y = -6 ==> y = -6/-3 = 1

etc...do the same with the y term and use tha same method for your problem 2)

Answer 5

You mean the system of equations?

1.
Change the 1st to:
-2x-10y=-14
2x+7y=8
-3y=-6
y=2
x+10=7
x=-3
(-3,2)
2.
Change both equations:
15x+25y=80
-15x+21y=12
46y=92
y=2
3x+10=16
3x=6
x=2
(2,2)