Solve the following simultaneous equations. 2x – 3y = 5 , x – 2y = 4
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We have to solve the following set of simultaneous equations:
2x - 3y = 5 ...(1)
x - 2y = 4 ...(2)
From (2)
x - 2y = 4
=> x= 4 + 2y
Substitute in (1)
2( 4 + 2y) - 3y = 5
=> 8 + 4y - 3y = 5
=> y = -3
x = 4 + 2y
=> x = 4 + 2*(-3)
=> x = 4 - 6
=> x = -2
We get x = -2 and y = -3
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x - 2y =4
x = 4 + 2y
2(4 + 2y) - 2y = 5
simplify:
8 + 4y -2y = 5
combine
8 + 1y =5
subtract 8
y = 5 - 8
y = -3
x – 2(-3) = 4
x + 6 = 4
subtract 6
x = -2
(-2, -3)
2x – 3y = 5 , x – 2y = 4
I am going to solve the second problem first to start:
x - 2y =4
add the 2y
x = 4 + 2y
now you know what x is so replace those numbers as x in the first problem:
2(4 + 2y) - 2y = 5
now simplify:
8 + 4y -2y = 5
combine like terms
8 + 1y =5
subtract the 8
y = 5 - 8
y = -3
now plug in y into any one of the problems to get x
x – 2(-3) = 4
x + 6 = 4
now subtract 6
x = -2
so (-2, -3)
We'll solve the system using elimination method. For this reason, we'll multiply by -2 the second equation:
-2x+4y=-8 (3)
We'll add (3) to (1):
-2x+ 4y + 2x – 3y = -8+5
We'll eliminate x and we'll combine like terms:
y = -3
We'll substitute y in (2):
x – 2*(-3) = 4
x + 6 = 4
x = 4 - 6
x = -2
The solution of the system is represented by the pair of coordinates: (-2 ; -3).
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