Solve the system using any method?

Question

Solve the system using any method.

5x+y=19
-x+2y=-6

A. (0,-3)
B. (2,0)
C. (3,4)
D. (4,-1)

Answer 1

substitute Method

5x + y = 19- - - - - - -Equation 1
- x + 2y = - 5- - - - - -Equation 2
- - - - - - - - - - -

isolate the y variable in equation 1

5x + y = 19

Transpose 5x

5x + y - 5x = - 5x + 19

y = - 5x + 19

substitute the y value into equation 2

- - - - - - - -- -

- x + 2y = - 6

- x + 2( - 5x + 19) = - 6

- x + ( - 10x + 38) = - 6

remove parenthesis

- x - 10x + 38 = - 6

Collect like terms

- 11x + 38 = - 6

Transpose 38

- 11x + 38 - 38 = - 6 - 38

- 11x = - 44

Divide both sides of the equation by - 11

- 11x / - 11 = - 44 / - 11

x = - 44 / - 11

x = 4

Insert the x value intko equation 1

- - - - - - - - - - - -

5x + y = 19

5(4) + y = 19

20 + y = 19

Transpose 20

20 + y - 20 = 19 - 20

y = 19 - 20

y = - 1

Insert the y value into equation 1
- - - - - - - - -

Check for equation 1

5x + y = 19

5(4) + ( - 1) = 19

Remove parenthesis'

20 - 1 = 19

19 = 19
- - - - - - - - -

Check for equatio 2

- x + 2y = - 6

- (4) + 2(- 1) = - 6

- 4 + (- 2) = - 6

Remove parenthesis

- 4 - 2 = - 6

- 6 - - 6

- - - - - - - - -

Both equations balance

The solution set is { 4, - 1 }

- - - - - - - - -s-

Answer 2

To do it by the substitution method, first look carefully at the

equations, and identify the one which, when substituted, will

be the easier of the two to calculate.If you re-arrange 5x+y=19

then you end up with either y=19-5x, or x=[19-y]/5, which will

involve substituting into -x+2y=-6, a bit more complex than

need be. If you re-arrange -x+2y =-6, for x, then you have

x=2y+6, so your substitution no longer involves so many minus

signs, thus making it easier, and fewer possibilities of

making mistakes. You should approach any problem

involving simultaneous equations in the same way, if you

intend to solve them by substitution.

Answer 3

5x+ y =19........(1)
-x +2y = -6........(2)
To eliminate y , the equation (1) x 2
10x + 2y = 38....(3)
Subtracting (2) from (3)
11x = 44
x = 44/11= 4
Substituting the value of x in eqn (1)
5*4 + y = 19
20 + y = 19
y = 19 - 20 = -1

Hence, the choice D, ie. x = 4 & y = -1, is correct....Ans

Answer 4

Multiply first equation by -4 -12x +16y = -4 then ADD THE TWO EQUATIONS 12x - y = -11 15y = -15 divide both sides by 15 y = -1 substitute -1 for y to solve for x 3x - 4(-1) = 1 3x +4 = 1 subtract 4 from both sides 3x = -3 divide both sides by 3 x = -1 (-1, -1)

Answer 5

5x+y=19.....(1)
-x+2y= -6.......(2)
From (1),we get
y=19-5x
Substituting this value of y in eqn(2)
-x+2(19-5x)=-6
or -x+38-10x= -6
or,-11x=-6-38= -44
or x=-44/-11=4
Putting the value of x=4 in y=19-5x
y=19-5*4=19-20= -1
x=4 and y= -1 ans

Answer 6

5x + y = 19
y = 19- 5x ........1

-x +2y = -6

-x + 38 - 10 x = -6

38 + 6 = 11x
44 = 11x

x = 4 ---------------
y=19- 5x = 19 - 20 = -1 ------------

The correct answer is D

Answer 7

The answer is D.(4,-1)
in the first case, as x=4 and y=-1,
5*4 + (-1) =19, proven.
-(4) + 2*(-1) = -6, also proven.

Answer 8

5x+y=19.....(1)
-x+2y=-6........(2)

Multiply (1) by 2
10x+2y=38.........(3)

Subtract (2) from (3)
10x-(-x)=38-(-6)
11x=44
x=44/11
x=4
Plug it into (1)
5*4+y=19
20+y=19
y=19-20
y=-1
The ans. is D. (4,-1)

Answer 9

5x+y=19 ---------------(1)
-x+2y=-6 --------------(2)

multiply eq(2) with 5

5x+y=19 ------------(1)
-5x+10y=-30 ------------(3)

adding (1)&(3)
11y=(-11)
y=(-1)

Substituting the value of y in eq(2),we get
-x+2*(-1)=-6
-x-2=-6
-x=-4
x=4

ANSWER: D. (4,-1)

Answer 10

5x + y = 19
-5x + 10y = - 30-----ADD
11y = - 11
y = - 1
5x - 1 = 19
5x = 20
x = 4
ANSWER D