Question 602995: Hello my name is Shamaila and I have problem solving these problems. 1. 5x-3y=1 y=3x-7
2. x=2y-10 4x-y=-47 3. 6x+5y=7 3x-7y=13 4. x-y=3 2x=4+2y 5. y=3x-2 y=2x-9 6. -2x+y=7 4x=2y-14
I will really really appreciate if anyone helps me solve these problems i dont know how to do them. Thank you so much!
My email address is bklynzkuri420@yahoo.com I need it by tonight thank you!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! We can solve these using two methods: substitution or elimination
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We will solve the first two using substitution
I will do the 1st one step-by-step
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1.
5x - 3y = 1
y = 3x - 7
Replace y in the 1st equation with (3x-7)
5x - 3(3x-7) = 1
5x - 9x + 21 = 1
-4x = 1 - 21
-4x = -20
x = -20/-4
x = +5
Use the 2nd equation to find y, replace x with 5
y = 3(5) - 7
y = 15 - 7
y = 8
Check the solutions in the 1st equation:
5(5) - 3(8) = 1
25 - 24 = 1; confirms our solutions of x=5; y=8
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2.
x = 2y - 10
4x - y = -47
Replace x in the 2nd equation with (2y-10)
4(2y-10) - y = -47
8y - 40 - y = -47
7y = -47 + 40
7y = -7
y = -1
Use the 1st equation to find x, replace y with -1
then check solutions in the 2nd equation
;
:
These equations can be done using elimination, will do the 1st one step-by-step
3.
6x + 5y = 7
3x - 7y = 13
multiply the 2nd equation by 2, subtract the 1st equation
6x - 14y = 26
6x + 5y = 7
-------------subtraction eliminates x, find y
0 - 19y = 19
y = 19/-19
y = -1
Find y using the 1st equation
6x + 5y = 7
Replace y with -1
6x +5(-1) = 7
6x - 5 = 7
6x = 7 + 5
6x = 12
x = 12/6
x = 2
Check solutions in the 2nd equation
3x - 7y = 13
replace x with 2, y with -1
3(2) - 7(-1) = 13
6 + 7 = 13, confirms our solutions of x=2, y=-1
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4.
x - y = 3
2x = 4 + 2y
Simplify, divide by 2, you then have
x = 2 + y
replace x with (2+y) in the 1st equation
(2+y) - y = 3
2 + y - y = 3
2 = 3; obviously there is no solution for this system
:
5.
y = 3x - 2
y = 2x - 9
---------------Subtraction will eliminate y, find x
0 = x + 7
subtract 7 from both sides
-7 = x
Use the 1st equation to find y
y = 3(-7) - 2
y = -21 - 2
y = -23
Check solutions in the 2nd equation
-23 = 2(-7) - 9
-23 = -14 - 9; confirms our solutions of x=-7. y=-23
:
6.
-2x + y = 7
4x = 2y - 14
arrange the 2nd equation for elimination
4x - 2y = -14
Simplify, divide by 2, add the 1st equation
2x - y = 7
-2x + y = -14
-----------------addition eliminates both variables,
0 + 0 = -7
another system with no solution
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