Solve the following systems of linear equations, showing all work: 5y+9x=27 8yx=70
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5y + 9x=27
8y  x=70
First find opposites.
You can do this by multiplying the second equation by 9 getting
72y  9x = 630
Now add this to the first equation. (Add the y terms together, the x terms together and the constants together. You should find the x terms cancel each other out.)
5y + 9x=27
72y  9x = 630
67y = 603
y = 9
Now that you know the value of y, plug the value into both equations...hopefully getting the same answer.
5(9) + 9x = 27 8(9) x = 70
45 + 9x = 27 72  x = 70
9x = 18  x = 2
x = 2 x = 2
Your point of intersection is (2, 9). This is also your solution to the system.
The given simultaneous equations are:
 5y + 9x = 27 ... (1)
8y  x = 70 ... (2)
We solve these equations for values of x an y as follows:
Multiplying equation (2) by 9 we get:
72y  9x =  630 ... (3)
Adding equation (1) and (3) we get:
 5y + 72y + 9x  9x = 27  630
67y = 603
Therefor:
y =  603/67 = 9
Substituting this value of y in equation (2) we get:
8*(9)y  x = 70
72  x = 70
 x =  70 + 72 = 2
Therefor x = 2
Answer:
x = 2, and y = 9
5y+9x=27..........(1)
8yx=70.............(2)
To solve the equations, we use 2nd equation. 8yx= 70. So x =708y .Or x=70+8y . We substitute 70+8y for x in eq (1):
5y+9(708y) =27.
5y+630+72y = 27.Or
67y = 27630 = 603. Or
y =603/67=9
y=603/67=9. Again substituting 9 for x in any of the two given equations,(we substitute in) 2nd eq: 8yx=70. Or 8*(9) =70. Therefore, 72x=70. Or x= 70+72 =2. So x=2.
