Solve this Simultaneous Equation?

Question

Showing all your working, solve this simultaneous equation:
3x -4y = 23
5x +2y = 21

Thanks to Dude2001 for the first correct answer B-)

Answer 1

Substitution Method

3x - 4y = 23- - - - - -Equation 1
5x + 2y = 21- - - - - Equation 2
- - - - - - - - - - -

Isolate the y variable in equation 2

5x + 2y = 21

Transpose 5x

5x + 2y - 5x = - 5x + 21

2y = - 5x + 21

Divide both sides of the equation by 2

2y / 2 = - 5x / 2 + 21 / 2

y = - 5/2x + 21/2

Substitute the y value into equation 1
- - - - - - - - - - - -

3x - 4y = 23

3x - 4( - 5/2x + 21/2) = 23

3x - ( - 20/2x + 84/2) = 23

3x - (- 10x + 42) = 23

Remove parenthesis

3x + 10x - 42 = 23

Colllect like terms

13x - 42 = 23

Transpose 42

13x - 42 + 42 = 23 + 42

Collect like terms

13x = 65

Divide both sides of the equation by 13

13x / 13 = 65 / 13

x = 65 / 13

x = 5

Substitute the x value into equation 1
- - - - - - - - - - - -

3x - 4y = 23

3(5) - 4y = 23

15 - 4y = 23

Transpose 15

15 - 4y - 15 = 23 - 15

collect like terms

- 4y = 8

Divide both sides of the equation by - 4

- 4y / - 4 = 8 / - 4

y = - 8/4

y = - 2

Substitute the y value into equation 1
- - - - - - - - - - -

Check for equation 1

3x - 4y = 23

3(5) - 4(- 2) = 23

15 - ( - 8) = 23

15 + 8 = 23

23 = 23
- - - - - - - - - -

Check for equation 2

5x + 2y = 21

5(5) + 2(- 2) = 21

25 + (- 4) = 21

25 - 4 = 21

21 = 21
- - - - - - - - -

Both equations balance

The solution set is { 5, - 2 }

- - - - - - - - - - - -s-

Answer 2

Let 3x -4y = 23 be [a] and 5x +2y = 21 be [b].

Multiply [b] by 2 on both sides:
2 * (5x +2y) = 2 * 21
So, 10x +4y = 42.
Let this be [c].

Add [a] and [c]
{3x -4y} + {10x +4y} = 23 + 42
So, 13x = 65
So, x = 5.

Put this value of x in [a]
3(5) -4y = 23
15 - 4y =23
-4y = 23 -15
-4y = 8

So y = -2

Solution set (5, -2)

Answer 3

3x-4y=23.................(1)
5x+2y=21.................(2)

now multiply equ (2) by 2

3x-4y=23................(3)
10x+4y=42.................(4)


now add the equ (3) and (4)

13x+0y=65.......................(5)
13x=65
x=65/13
x=5...............answer for x


now put the value of x in eqution (1)


3*(5)-4y=23 (by putting the value of x from above eqution)
15-4y=23 (changing the side for 4y)
4y=15-23
4y=(-8)
y=(-2)

y=(-2).........answer for y


hence the answer is x=5,y=-2

for checking the correct answer put the value in eqution 1 or 2
and the lhs=rhs(that is the eqution is equate)

3*5-4*(-2)=23
15+8=23
23=23
for other equation(2)

5*5+2*(-2)=21
25-4=21
21=21



hence proved and the answers are correct.

Answer 4

5(3x-4y = 23)....(1)
3(5x +2y = 21)...(2)

Process of elimination:
15x - 20 y = 115.....(3)
- 15x + 6y = 63..........(4)

=> -26y = 52......(5)
y = 52/ -26
y = -2

substitute (-2) for y in eqn. 3
15x - 20(-2) = 115
15x + 40 = 115
15x = 115 - 40
15x = 75
x = 75/15
x = 5.

so x = 5; y = -2

Answer 5

3x - 4y = 23
10x + 4y = 42----ADD
13x = 65
x = 5

25 + 2y = 21
2y = - 4
y = - 2

x = 5 , y = - 2

Answer 6

3x - 4y = 23 ---------------(1)
5x + 2y = 21 ---------------(2)

Mutiplying eq. (2) by 2 :
10x + 4y = 42 ---------------(3)

Adding eq. (1) & (3) :
13x = 65
x = 5

Substituting x = 5 in eq. (1) :
3(5) - 4y = 23
15 - 4y = 23
4y = - 8
y = -2

Ans. x = 5 & y = -2

Answer 7

multiply the second equation by 2, that cancels out the y terms when you add the equations. remember, if you have an equation and you multiply or divide both sides by the same term, the equality is still valid.