can you please help me solve these simultaneous equationsy=x+1 and y=-2x-4            y=3x-5 and 2y+x=4

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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Here's how to do this.

For the first equation, you have two equations that both equal y.  Therefore they equal each other.  So you set it up as

(x+1) = (-2x-4)

So you just get the variables on one side and the numbers on the other.

3x = -5 or x = -5/3

You could then just plug that in for x to solve for y

y = (-5/3)+1 or y = -2/3

The second one is a little harder but all you have to do is substitute for y in the second equation.  You know that y = 3x-5 so therefore

2(3x-5) + x = 4

6x - 10 + x = 4

7x = 14

x = 2

Again, you can plug this in to solve for y.

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malkaam | Student, Undergraduate | (Level 1) Valedictorian

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  1.     y=x+1 and y=-2x-4           

y=x+1   ------(i)

y=-2x-4 ------(ii)

Consider eq(i)

y=x+1  

Input the value of y in eq(ii)

y=-2x-4 

x+1=-2x-4

x+1-1=-2x-4-1         Subtract 1 from both sides

x=-2x-5

x+2x=-2x-5+2x       Add 2x

3x=-5

3x/3=-5/3                Divide both sides by 3

x=-5/3

Then input this value in eq(i)

y=x+1  

y=-5/3+1

y=-5+3/3

y=-2/3

Therefore

x=-5/3

y=-2/3 Answer.

  1.     y=3x-5 and 2y+x=4

y=3x-5   ------(i)

2y+x=4  ------(ii)

Consider eq(i)

y=3x-5

Input this value in eq(ii)

2y+x=4 

2(3x-5)+x=4

6x-10+x=4

7x-10+10=4+10           Add 10 to both sides

7x=14

7x/7=14/7                     Divide both sides by 7

x=2

Now input this value in eq(i)

y=3x-5  

y=3(2)-5

y=6-5

y=1

Therefore

x=2

y=1 Answer.

If you want to check if they are correct you can input the values in the equations and see if they are equal.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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(1)  y = x + 1
(2)  y = -2x - 4

(1) = (2)
x + 1 = -2x - 4

Now its a single variable equation and you can solve for x. Plug in this x value into one of your equations to find y.

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

Substitute (1) into (2)

2(3x - 5) + x = 4

Now its a single variable equation and you can solve for x. Plug in this x value into one of your equations to find y.

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itssnigdha | Student, Grade 11 | (Level 2) Honors

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1.

y=x+1..(i)     y=-2x-4...(ii)

From (i) & (ii)--

y=x+1=-2x-4

x+1=-2x-4

=> x+2x=-4-1

=> 3x=3

=> x=3/3

=> x=1.

y=x+1..(i)

=1+1

=> y=2.

 

2.

y=3x-5..(i)   2y+x=4

=> 2y=-x+4

=> y=(-x+4)/2...(ii)

From (i) & (ii)--

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

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

=> 2(3x-5)=-x+4

=> 6x-10=-x+4

=> 6x+x=4+10

=> 7x=14

=> x=14/7

=> x=2

y=3x-5..(i)

=(3*2)-5

=6-5

=> y=1

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

1)y=x+1 and y=-2x-4

Another common method is substitution.

We'll write an unknown from one equation, depending on the other unknown, like in this case:

 y=x+1

x=y-1

We'll substitute this expression into the second equation:

 y=-2x-4    , but  x=y-1

y=-2(y-1)-4

y=-2y+2-4

We'll move the unknown "-2y" to the left side:

y+2y=-2

3y=-2

y=-2/3

With the value for "y", we'll go into the expression for x:

 x=y-1

x=(-2/3)-1

x=-5/3

2)y=3x-5 and 2y+x=4

In this group of simultaneous equations you can choose to express the unknown "y", in the second equation,2y+x=4.

2y+x=4

2y=-x+4

y=(4-x)/2

The first equation is written depending on the unknown "y":

y=3x-5, but, from re-writting the second equation: y=(4-x)/2

Because the equations are simultaneous, that means:

3x-5=(4-x)/2

We'll cross multiplying, so that:

(3x-5)*2=(4-x)

6x-10=4-x

6x+x=4+10

7x=14

x=14/7

x=2

Now all you have to do is to substitute the found value for x into whatever equation you desire:

  y=3x-5 , x=2

  y=3*2-5

  y=6-5

y=1

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neela | High School Teacher | (Level 3) Valedictorian

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

To find x and y:

Solution:

There are 2 pairs of simultaneous equations of two variables. The technic is normally by eliminating one variable  or by substution of one variable by another variable. Thus we reduce the variables to one single variable and one single equation and solve the unknown. And then use the given given equation by substituting the one value of the variable so found and find the value of the other variable.

1)

y=x+1..............................(i) and

y=-2x-4 ..........................(ii).

This is a pair of simultaneous equations with two variables, x and y. The left side of both equations are equal to y. Therefore, the right side must be equal:

x+1=-2x-4 or

x+2x=-1-4 =- 5 or

3x=-5 or x=-5/3. So from (1) y= x+1 = -5/3+1 =-2/3.

The method is as good as the substitution of y  from 1st  in to the 2nd.

It is not necessary that we should eliminate  y 1st and we should solve for x first. But it is obviously easier  to so.

y=x+1  or x=y-1 could be substited in the 2nd equation,y =-2x-4. So y=-2(y-1)-4 or y=-2y+2-4 or 3y =-2 or y= -2/3. And substituting in   y=x+1  or in  x=y-1, we get x=-2/3-1 =-5/3

2)

y=3x-5....................................(i)and

2y+x= 4...................................(ii).

Using substitution  for y=3x-5 from in equation,(2) we get:

2(3x-5)+x =4 or

6x-10+x= 4 or

6x +x  = 4+10 or

7x=14 or

x= 14/7 = 2,  and from equation (i),

y=3x-5 = 3*2- 5 = 1

 

 

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