# 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**

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).**