Simultaneous Equations

Simultaneous Equations

If X + Y = 5, what are the values of X and Y?

Is it X = 4, Y = 1 ?

(or) X = 3, Y = 2 ?

(or) X = 2.5, Y = 2.5 ?

To find unique values of X and Y, we need one more equation, say X – Y = 3.

Equations X + Y = 5 and X – Y = 3 are called as Simultaneous Equations.

The solution of above equations is X = 4 and Y = 1.

How to find these values of X and Y?

Solving Simultaneous Equations by Substitution

Use an equation to find one variable in terms of another variable and substitute in the other equation.

X + Y = 5 ….(1)

X – Y = 3 ….(2)

From (2), we get, X = 3 + Y

Substitute X = 3 + Y in (1)

3 + Y + Y = 5

3 + 2Y = 5

2Y = 5 – 3

2Y = 2

Y = 1

Substitute Y = 1 in (1),

X + Y = 5

X + 1 = 5

X = 5 – 1

X = 4

Solving Simultaneous Equations by Elimination

By adding or subtracting given equations, eliminate one variable.

Before add or subtract, make the coefficient of the variable you wish to eliminate equal in both equations.

X + Y = 5 ….(1)

X – Y = 3 ….(2)

(1) + (2), 2X = 8

X = 8/2 = 4

Substitute X = 4 in (1),

X + Y = 5

4 + Y = 5

Y = 5 – 4

Y = 1

Solving Simultaneous Equations by Drawing Graphs

Questions

1. 2 Pens and 3 Pencils costs $2.60. 3 Pens and 2 Pencils cost $3.40. Taking cost of a Pen as $x and cost of a Pencil as $y, form two equations in x and y. Solve these equations and find the cost of a Pen.

2. A Skirt costs $5 more than a Blouse. 3 Skirts and 2 blouses cost $55. Taking cost of a Skirt as $S and cost of a Blouse as $B, form two equations in S and B. Solve these equations and find the cost of a Blouse .