i) Solve the simultaneous equations 4x + 3y + 4 = 0, 3x - 12y + 22 = 0. Could you please teach me step by step, so that I can understand easily and without any problem? Thank you. :)
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4x + 3y + 4 = 0, 3x - 12y + 22 = 0.
I think the easiest way to do this is by addition. So we need to make it so two of the variables (one each from each equation) will come to 0 when we add them.
I think the best way to do this is to multiply the first equation by 4 because then we will have 12y to cancel the -12y in the other equation.
So we multiply by 4 and we have
16x + 12y + 16
Now we add that equation to the other. We add the like terms together.
16x + 3x is 19x
12y + (-) 12 y is 0
16 + 22 is 38.
So we have 19x + 38 + 0
Move the 38 to the other side, we have
19x = -38
x = -2
Substitute that back into the first equation to solve for y.
4(-2) + 3y +4 = 0
-8 +3y +4 + 0
3y = 8 - 4
3y = 4
y = 4/3
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(1) 4x + 3y + 4 = 0
(2) 3x - 12y + 22 = 0
Multiply (1) by 4
(3) 16x + 12y + 16 = 0
Add (3) and (2)
19x + 38 = 0
Now its single variable and you can solve for x. Plug this value into one of the equations (1) or (2) and solve for y.
y=4/3
16x + 12y + 16
16x + 3x is 19x
12y + (-) 12 y is 0
16 + 22 is 38.
19x + 38 + 0
19x = -38
x = -2
To solve for y:
4(-2) + 3y +4 = 0
-8 +3y +4 + 0
3y = 8 - 4
3y = 4
y = 4/3
I hope I helped you. Bye!
4x+3y+4=0..............(1)
3x-12y+22=0...........(2) are the two equations given to be solved for x and y.
From eq(1) we get: 3y = -(4x+4) Or
y = -(4x+4)/3. Substituting in eq(2) y = -(4x+4)/3, we get:
3x-12[-(4x+4)/3]+22=0. Or
3x+4(4x+4)+22 = 0. Or
19x +38 = 0 Or
x = -38/19 = -2. Substituting this value of x = -2 in (1),
4(-2)+3y+4= 0. Or
3y = 4 or y = 4/3
The given simultaneous equations are:
4x + 3y + 4 = 0 ... (1)
3x - 12y + 22 = 0 ... (2)
Multiplying equation (1) by 4 we get:
16x + 12y + 16 = 0 ... (3)
adding equation (2) and (3) we get:
3x + 16x - 12y + 12y + 22 + 16 = 0
19x + 38 = 0
19x = -38
Therefore:
x = -38/19 = -2
Substituting this value of x in equation (1) we get:
4*(-2) + 3y + 4 = 0
-8 + 3y + 4 =0
3y = 4
Therefore:
y = 4/3
Answer:
x = -2, and y = 4/3
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