Maths- simultaneous equations question?

(10x+4y = 3) * 5 = 50x + 20y = 15


(50x + 20y = 15) + (5x - 20y = - 4)

= 55x = 11
x = 11/55 = 1/5 = 0.2

substituting x we get y

so (5 * 0.2) - 20y = -4
1- 20y = -4
1 = -4 + 20y
1+4 = 20y
5 = 20y
y = 5/20 = 1/4

1st equation for y:
10x + 4y = 3
4y = 3 - 10x
y = 3/4 - 5/2x

2nd equation for x (plug y):
5x - 20(3/4 - 5/2x) = - 4
5x - 15 + 50x = - 4
55x = 11
x = 1/5

1st equation for y (plug x with 1/5):
= 3/4 - 5/2(1/5)
= 3/4 - 1/2
= 3/4 - 2/4
= 1/4 or

5(1/5) - 20y = - 4
1 - 20y = - 4
20y = 5
y = 5/20 or 1/4

Answer: x = 1/5, y = 1/4

Turkey - why are you copying off 'Mystery name'?

multiply 5x-20y=-4 by -2 to get -10x +40y =8. now add this equation to 10x +4y =3. so we get

10x+4y =3
-10x +40y =8
_____________
ox +44y = 11
44y =11
divide both sides by 44
so y = 11/44 = 1/4.


now go back to 10x+4y=3 and substitute y = 1/4
so you get
10x + 4(1/4) = 3
this gives
10x + 1 =3
10x =2
x = 2/10 =1/5
done

We can do elimination to solve for the value of x and y. It means we either eliminate x or y. In this case, let's eliminate x since we just need to multiply the 2nd eqn by -2 and proceed to addition of the two eqns

10x+4y = 3
+[-2(5x-20y) = -4]

Distributing -2

10x+4y = 3
-10x+40y = 8
______________
0 + 44y = 11

0 + 44y = 11
44y = 11
y = 1/4

Substitute this value to any eqn since the result will just be the same
Substituting to the first eqn
10x + 4(1/4) = 3
10x + 1 = 3
10x = 2
x = 2/10 = 1/5

Ans: x = 1/5 ; y = 1/4

multiple equation 2) by 2 to give,
1) 10x+4y = 3
2) 10x-40y = -8
the subtract 1) - 2)
44y = 11
y = 1/4
now sub y into equation 1)
10x +1 = 3
10x = 2
x = 1/5

10x + 4y = 3
5x - 20y = -4

5x - 20y = -4
5x = -4 + 20y
2(5x) = 2(20y - 4)
10x = 40y - 8

10x + 4y = 3
(40y - 8) + 4y = 3
40y + 4y - 8 = 3
44y = 3 + 8
44y = 11
y = 11/44
y = 1/4 (0.25)

10x + 4y = 3
10x + 4(1/4) = 3
10x + 1 = 3
10x = 3 - 1
x = 2/10
x = 1/5 (0.2)

∴ x = 1/5 (0.2) , y = 1/4 (0.25)

50x + 20 y = 15
5x - 20 y = - 4-----ADD

55x = 11
x = 11 / 55
x = 1 / 5

2 + 4 y = 3
4 y = 1
y = 1 / 4

x = 1 / 5 , y = 1 / 4

(10x+4y = 3) * 5 = 50x + 20y = 15


(50x + 20y = 15) + (5x - 20y = - 4)

= 55x = 11
x = 11/55 = 1/5 = 0.2

substituting x we get y

so (5 * 0.2) - 20y = -4
1- 20y = -4
1 = -4 + 20y
1+4 = 20y
5 = 20y
y = 5/20 = 1/4