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Simple Equations

    Review of What We Know

    What Have We Discussed ?

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7th class > Simple Equations > Review of What We Know

Review of What We Know

An equation is a mathematical statement that asserts two expressions are equal, with conditions imposed on variables.

For example: in the equation 2a+8=18, the variable is 'a'. This equation means if we double 'a' and add 8, we get 18.

Variables in Equations

What is a Variable?

A variable represents a number that can vary or change. In equations, variables are usually represented by letters like x, y, z, a, b, etc.

In our examples, 'a' in 2a + 8 = 36 and 'b' in 5b - 15 = 35 are variables.

Creating Expressions Using Variables:

Expressions are formed by performing operations such as addition, subtraction, multiplication, or division on variables.

From 'a', we create the expression 2a + 8 by first multiplying 'a' by 2, then adding 8. Similarly, 5b - 15 is formed by multiplying 'b' by 5 and subtracting 15.

Dependence of Expression Values on Variables:

The value of an expression changes depending on the value of the variable.

For instance, if a = 10 in the expression 2a + 8, it becomes 2 × 10 + 8, which equals .

Finding Solutions to Equations:

Solving an equation like 2a + 8 = 36 or 5b - 15 = 35 involves finding the values of 'a' and 'b' that make these statements true. It's a way of determining how a variable is related to other numbers in the context of the given equation.

Instruction

Consider the equation 10y - 20 = 50.

The value of the expression (10y – 20) depends on the value of .

Let's verify this by giving five different values to y and finding for each y, the value of 10y−20.

For the expression 10y−20,
Let's evaluate it for five different values of y : 1, 3, 5 and 7.
For y = 1: 10 × 1 − 20 = .
For y = 3: 10 × 3 − 20 = .
For y = 5: 10 × 5 - 20 = .
For y = 7: 10 × 7 − 20 = .
So we see that when y takes the value , the equation 10y−20 = 50 becomes true. So we say that y = 7 solves the equation 10y−20=50.
Since the expression 10y−20 increases by 10 for each increment in y, we call it as linear relation.