SOLUTION: Hi can you please help me in solving these equations thank you 1.what are the values of x and y if the following are both true 3x

SOLUTION: Hi can you please help me in solving these equations thank you 1.what are the values of x and y if the following are both true 3x - 2y = 3 x + 4y = 29 2. which pair of

Question 62523: Hi can you please help me in solving these equations thank you
1.what are the values of x and y if the following are both true
3x - 2y = 3

x + 4y = 29
2. which pair of values satisfies the equation

4x - y = 12

3x - 2y = 14
3. Use the trial and improvement method to solve the equation 2x + 5 = 24. Find a solution that is a positive number and give your answer to 1 d.p.
* i could not fit the power of 3 on top of 2x so 2x has a power of three
Thank you hope you can help me answereing these 3 sets of questions for my homework
Answer by dolly(163) (Show Source): You can put this solution on YOUR website!
1)We have 2 equations with us
3x-2y=3 ---------(1)
x+4y=29 ---------(2)
From equation (2) we first find what is x
subtracting 4y on both sides
==> x+4y-4y=29-4y
==> x=29-4y -----(3)
We substitute this value of x in equation (1)
we get, 3(29-4y)-2y=3
==> 87-12y-2y=3
Subtracting 87 on both sides we get,
87-87-12y-2y=3-87
==> -12y-2y=-84
==> -14y=-84
Now dividing both sides by -14,
(-14/-14)y=(-84/-14)
==> y=+6
From (3) we substitute the value oy y=6 to find x
==> x=29-4y
==> x=29-(4*6)
==> x=29-24
==> x=+5
The values of x and y are +5 and +6.

2) We have 2 equations with us
4x-y=12---------(1)
3x-2y=14 ---------(2)
From equation (1) we find what y is
subtracting 4x on both sides, we get
-4x+4x-y=12-4x
==> -y=12-4x
Dividing by -1 on both sides we get
-y/-1=(12-4x)/-1
==> y=-12+4x ----(3)
Substituting this value of y in equation (2)
3x-2(-12+4x)=14
==> 3x+24-8x=14
==> -5x+24=14
subtracting -24 on both sides, we get

-24+24-5x=14-24
==> -5x=-10
Dividing on both sides by -5,
-5x/-5=-10/-5
==> x=2
Substituting this value of x in equation (3)
==> y=-12+4x
==> x=-12+4*2
==> x=-12+8
==>x=-4
The values of x and y are 2 and -4.

3) 2x+5=24 where 2x is to power 3
2x^3+5=24
subtracting 5 on both sides
2x^3+5-5=24-5
==> 2x^3=19
dividing by 2 on both sides we get,
(2x^3)/2=19/2
==> x^3=9.5
Finding the cube root of 9.5 we get the value of x
==> x=2.1

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