Solve the simultaneous equations 4x+y=-1 4x+3y=7

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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The way to solve this sort of set of equations is to substitute a value for one of the variables.

If you look at the first equation, you see that you can easily get a value for y.  You do that by subtracting 4x from both sides of the equation.

That gives you

y = 1-4x

So now you take that value for y and plug it in to the other equation:

4x + 3 (1-4x) = 7

4x +3 - 12x = 7

4x - 12 x = 4

-8x = 4

x = -.5

Now you can plug that value back into the first equation.

4 (-.5) + y = 1

-2 + y = 1

y = 3

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Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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This answer is incorrect because the first subtraction was done incorrectly. It should be y = -1 - 4x.

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

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4x+y=-1 ----(i)

4x+3y=7 ----(ii)

Taking equation (i) to isolate y:

4x + y = -1

y = -1 -4x

Putting this value in (ii):

4x + 3 (-1-4x) = 7

4x -3 -12x = 7

-8x -3 = 7

-8x = 7+3

-8x = 10

x = - 10/8

x = - 5/4

Now, putting value of x in (i) to find out y:

4(-5/4) +y = -1

-5 +y = -1

 y = -1 +5

y = 4

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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Elimination method is easiest here.
(1) 4x + y = -1
(2) 4x + 3y = 7

(2) - (1)
2y = 8
=> y = 4

Plug this into equation 1 and solve for x.

4x + 4 = -1
4x = -5
x = -5/4

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The two simultaneous equations are:

4x + y = -1      ... (1)

4x + 3y = 7      ... (2)

Subtracting equation (1) from equation (2) we get:

4x - 4x + 3y - y = 7 + 1

2y = 8

Dividing both sides of above equation we get:

y = 4

Substituting this value of y in equation (1) we get

4x + 4 = -1

4x = -1 - 4 = -5

Dividing both sides of above equation by 4 we get:

x = -5/4 = -1.25

Answer:

x = -1.25, and y = 4

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

4x+y = -1 ...........(1)

4x+3y =7..............(2). Edited the equation as linear equation, originally given as 4x3y = 7

(2)-(1) eliminates x :

4x-4x+3y-y = 7- -1 =8 Or

2y = 8. Or y = 8/2 =4. Or

y=4

Substituteing y = 4 in (2), 4x+3*4 = 7. Therefore,

4x = 7-3*4 = -5. Or x = -5/4

So the solution to the simultaneous linear equations is x= -5/4 and y = 4

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