systems equations?

Question

6x+10y=7
15x-4y=3

please show working

Answer 1

Use one of them to get x to y relation and substitute x or y in the other. This way you can find the one unknown and after substituting it with it's known value in the x/y relation you will find the other one.

There are other ways for dealing with system equation, but this one suits your system best.

Try to make it yourself. This is the best way to learn.

Answer 2

6x + 10y = 7. . . .. equation 1
15x - 4y = 3. . .. . equation 2
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Multiply equation 1 by 2 and equation 2 by 5

2(6x) + 2(20y) = 2(7)

12x + 20y = 14. . .New equation 1

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15x - 4y = 3

5(15x) - 5(4y) = 5(3)

75x - 20y = 15. . . .New equation 2

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Elimination of y new equation 1 and new equation 2

12x + 20y = 14
75x - 20y = 15
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87x = 29

87x/87 = 29/87

x = 29/87

The answer is x = 29/87

Insert the x value into equation 1

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6x + 10y = 7

6(29/87) + 10y = 7

174/87 + 10y = 7

2 + 10y = 7

2 + 10y - 2 = 7 - 2

10y = 5

10y/10 = 5/10

y = 5/10

y = 1/2

The answer is y = 1/2

Insert the y value into equation 1

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Check for equation 1

6x + 10y = 7

6(29/87) + 10(1/2) = 7

174/87 + 10/2 = 7

2 + 5 = 7

7 = 7

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Check for equation 2

15x - 4y = 3

15(29/87) - 4(1/2) = 3

435/87 - 4/2 = 3

5 - 2 = 3

3 = 3

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The solution set { 29/87, 1/2 }

The x value of 29/87 simplified to 1/3. 1/3 solution will work.

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Answer 3

6x+10y=7
15x-4y=3
in the first equation:
x=(7-10y)/6

then substitute this in the second equation:

15(7-10y)/6-4y=3 yuu can simplify this in this way:
5(7-10y)/2-4y=3

5(7-10y)=6+8y
35-50y=8y+6
35-6=8y+50y
29=58y
y=29/58
y=1/2

once you have obtained the value of y, which is 1/2, substitute it in the first equation:

6x+10y=7
6x+10/2=7
6x+5=7
6x=7-5
6x=2
x=2/6
x=1/3

solution:
y=1/2
x=1/3

Answer 4

6x + 10y = 7..... Eq 1
15x - 4y = 3..... Eq 2
Consider Eq 2
15x - 4y = 3
15x = 3 + 4y
x = (3 + 4y)/15
Substitute this value of 'x' in Eq 1
6x + 10y = 7
6[(3 + 4y)/15] + 10y = 7
2[(3 + 4y)/5] + 10y = 7
[2(3 + 4y)/5] + 10y = 7
(6 + 8y)/5 + 10y = 7
(6 + 8y)/5 + 50y/5 = 7
(6 + 8y + 50y)/5 = 7
(6 + 58y)/5 = 7
6 + 58y = 7*5
6 + 58y = 35
58y = 35-6
58y = 29
y = 29/58
y = 1/2
Now substitute this value in the derivation of 'x'
x = (3 + 4y)/15
x = (3 + 4*1/2)/15
x = (3 + 2)/15
x = 5/15
x = 1/3
(x = 1/3, y = 1/2)

Answer 5

6x+10y=7 . . (i)
15x-4y=3. . (ii)

(i) * 10 + (ii) * 4
we get
6*10x + 15*4x = 7*10 + 3*4
or,120x = 82
or, x = 41/60

y = (7-6y)/10 = 29/100