for the linear equation 1/2x-1/2y=2 and 4/3x+5y=-1 how do I find the solution (point that meets)?

Answer 1

1/2x - 1/2y = 2 - - - - - -Equation 1
4/3 x + 5y = - 1- - - - - -Equation 2
- - - - - - - - - - -
Multiply equation 1 by - 8 and clear the fraction equation 2

1/2x - 1/2y = 2

-8(1/2x) - (-8)(1/2y) = - 8(2)

- 8/2x - (-8/2y) = - 16

- 4x + 4y = - 16. . . New equation 1

- - - - - - - - -

4/3x + 5y = - 1

3(4/3x) + 3(5y) = 3(- 1)

4y + 15y = - 3 . . .New equation 2

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

- 4x + 4Y = - 16
4x + 15y = - 3
- - - - - - - - - -
19y = - 19

19y/19 = - 19/19

y = - 1

The answer is y = - 1

Insert the y value into equation 2

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

4/3x + 5y = - 1

4/3y + 5( - 1) = -1

4/3x + (- 5) = - 1

4/3x - 5 = - 1

4/3x - 5 + 5 = - 1 + 5

4/3x = 4

3(4/3x) = 3(4)

4x = 12

4x/4 = 12/4

x = 3

The answer is x = 3

Insert the x value into equation 2

- - - - - - - - - - -

Check for equation 2

4/3x + 5y = - 1

4/3(3) + 5( - 1) = - 1

12/3 + (-5) = - 1

4 - 5 = - 1

- 1 = - 1

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

Check for euation 1

1/2x - 1/2y = 2

1/2(3) - 1/2(- 1) = 2

3/2 - (-1/2) = 2

3/2 + 1/2 = 4

4/2 = 2

2 = 2

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

The solution set { 3, - 1 }

- - - - - - - -s-

Answer 2

300x+200y=500 divide by potential of one hundred 3 x + 2 y = 5 (a million) and 7x-5y=31 ( 2 ) multiply ( a million ) by potential of five snd ( 2 ) by potential of two 15 x + 10 y = 25 and 14 x - 10 y = sixty two upload the two equation 29x = 87 divide by potential of 29 x = 3 replace in ( a million ) 9 + 2y = 5 2y = 5 - 9 2y = - 4 divde by potential of two y = - 2 the answer is : b) (x,y)=(3,-2)

Answer 3

to find the intersecting points of the two equations, solve them simultaneously:

1/2x-1/2y=2 ------(1)
4/3x+5y=-1--------(2)

multiply eqaution (1) by 8:
4x -4y = 16----------(3)

multiply equation (2) by 3:
4x + 15y = -3------(4)

subtract eqaution (4) from (3) i.e. (3) -(4):

(4x-4y) - (4x+15y) = 16-(-3)
-19y = 19
y = -1

substitute y = -1 into equation (1):

1/2x - 1/2*(-1) = 2
1/2x + 1/2 = 2
1/2 x = 2-1/2 = 3/2
x = 3

therefore the point of intersection is given by the coordinates
(3, -1)

hope it helps!

Answer 4

(1/2x) - (1/2)y = 2
(4/3)x + 5y = -1
The quickest way looks to be substitution:
x/2 = 2 + y/2
x = 4 + y
4(4 + y)/3 + 5y = -1
16 + 4y +15y = -3
19y = -19
y = -1
x = 4 - 1
x = 3
x,y = (3,-1)

Answer 5

subtract them

1/2x-1/2y=2
-
4/3x+5y=-1
__________