How do i solve these and what method do i use :   (1)x=2y (2)3x+y =7 (1)3x+5y=2 (2)3x-3y=10 Simultaneous equations

Expert Answers
hala718 eNotes educator| Certified Educator

x= 2y.......(1)

3x+y = 7........(2)

First let us substitute (1) in (2)

x= 2y ==> 3x + y = 7

==> 3(2y) + y= 7

==> 6y + y = 7

==> 7y= 7

==> y = 1

Now substitue in (1)

x= 2y

x= 2(1)

x= 2

3x + 5y = 2........(1)

3x-3y = 10.........(2)

Let us subtract (2) from (1)

==> 8y = -8

==> y = -1

Now substitute in (1)

3x + 5y = 2

3x + 5(-1) = 2

3x -5 = 2

3x = 7

x= 7/3

giorgiana1976 | Student

We'll solve the first system of equations using substitution technique:

x=2y

3*2y+y=7

6y+y=7

7y=7

y=1

Now, all we have to do is to put the found value for y into what equation we prefer.

x=2y

x=2*1

x=2

Let's solve the second system of equations:

3x+5y=2

3x-3y=10

We'll solve this system using the substitution method:

3x=2-5y

Now, instead of 3x, we'll write in the second equation 2-5y

2-5y - 3y =10

2-8y=10

8y=2-10

8y=-8

y=-1

We know that 3x=2-5y and y=-1.

3x=2-5*(-1)

3x=2+5

3x=7

x=7/3

neela | Student

a)

x=2y (1)and 3x+y =7.(2)

Use x=2y in (2). Then 3(2y) +y =7.

6y+y =7. 7y =7. y =1. So x = 2y = 2

x=2 and y = 1

b)

3x+5y =2 .(1)and 3x-3y =10...........(2)

Eq(1)- Eq(2): 8y = 2-10 = -8, x = -1

From (1) 3*(-1) +5y= 2

5y = 5

y =1.

x=-1 and y =1

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