pairs of equations???///???

Question

can sombody please help me learn how to solve problems like these.
2x+3y=13 and y=4x+1

7x-3y=31 and y-5=3x

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

Answer 1

Here is the way to do these problems. Solve for one of the variables in therms of the other and then substitute.
Substitute y = 4x + 1 for y in the first equation. You get:
2x + 3(4x +1) = 13
2x +12x + 3 = 13
14x = 10
x = 5/7

go back to the second and plug in x = 5/7 to find y

y = 4(5/7) + 1 = 27/7

Check solution by plugging in x = 5/7 and y = 27/7 in first equation:

2(5/7) + 3(27/7) = 10/7 +81/7 = 91/7 = 13

Now you do the other two.

Answer 2

Question 1
2x + 3.(4x + 1) = 13
14x + 3 = 13
14x = 10
x = 10 / 14 = 5 / 7
y = 20 / 7 + 1
y = 27 / 7
x = 5 / 7 , y = 27 / 7
Question 2
7x - 3.(3x + 5) = 31
- 2x = 46
x = - 23
y = - 69 + 5
y = - 64
x = - 23 , y = - 64
Question 3
4x - 3y = - 2
- 3x + 2y = - 3

8x - 6y = - 4
- 9x + 6y = - 9-----ADD
- x = - 13
x = 13
- 39 + 2y = - 3
2y = 36
y = 18
x = 13 , y = 18

Answer 3

2x+3y=13 and y=4x+1
Hhere you canuse substitution as follows:
2x +3(4x+1) = 13 [We substituted 4x=1 for y in 1st equation]
2x +12x +3 = 13
14x = 10
x = 10/14 = 5/7. So y = 4(5/7)+1 = 27/7 = 3 6/7

y-5 = 3x --> y = 3x+5
Now plug 3x+5 for y in the first equatio and solve as shown above

Multiply 1st equation by 2 getting 8x-6y = -4
Multiply 2nd equation by 3 getting 6y +9 = 9x
Now add thee two new equations getting 8x+9 =-4+9x
So x = 13 and y = (3*13-3)/2= 18
Notice how we eliminated y by multiplying each equation by a number that made the y terms equal and opposite and thus they dissappeared when added..

Answer 4

2x+3y=13 (I)
y=4x+1 (II)

2x + 3(4x + 1) = 13
2x + 12x + 3 = 13
14x = 13 - 3
14x = 10
x = 10/14
x = 5/7

y = 4x + 1
y = 4(5/7) + 1
y = 20/7 + 1
y = 27/7
Solution: {(5/7 and 27/7)}
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7x-3y=31 (I)
y-5=3x (II) y = 3x + 5

7x - 3(3x + 5) = 31
7x - 9x -15 = 31
-2x = 31 + 15
-2x = 46
x = 46 : -2
x = -23

y = 3x + 5
y = 3(-23) + 5
y = -69 + 5
y = -64
Solution: {(-23 and -64)}
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4x-3y = -2 (I)
2y+3=3x (II)

4x - 3y = -2 (I) (*2)
3x + 2y = -3 (II) (*3)

8x - 6y = -4 (I)
9x + 6y = -9 (II)
----------------
17x = 13
x = 13/17

8(13/17) - 6y = -4
104/17 - 6y = -4
-6y = -4 -104/17
y = -172/17 *-1/6
y = 86/51
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Answer 5

well first you need to transpose the equations so you have y=............ the one way you could work out x would be to put them together, so they equal each other and transpose that to make x=............ then put the x number back into one of the equations (the easiest one) to find y.
so with the first 1
2x+3y=13
3y=13-2x
y=(13-2x)/3

then

(13-2x)/3=4x+1
13-2x=12x+3
-2x=12x+3-13
-14x=-10
x=5/7

then sub that number intoo y=4x+1

so
y=4(5/7)+1
y=27/7
=3 6/7