Discussion Topic

# Solving simultaneous equations

Summary:

To solve simultaneous equations, use methods such as substitution, elimination, or graphical representation. Substitution involves solving one equation for one variable and substituting this value into the other equation. Elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other. Graphical representation involves plotting both equations on a graph and finding their intersection point.

Solve the following simultaneous equations. 2x – 3y = 5 , x – 2y = 4

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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Solve the following simultaneous equations. x + 3y = 2 , 2x + 8y = 6

We have to solve the following set of simultaneous equations:

x + 3y = 2 ...(1)

2x + 8y = 6 ...(2)

2*(1) - (2)

=> 2x + 6y - 2x - 8y = 4 - 6

=> -2y = -2

=> y = -2/-2

=> y = 1

substitute in (1)

x + 3 = 2

=> x = 2 - 3

=> x = -1

We get x = -1 and y = 1

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