Class 7 Exam > Class 7 Videos > Equation that describes number pairs - Math, Class 7
Equation that describes number pairs - Math, Class 7 Video Lecture
FAQs on Equation that describes number pairs - Math, Class 7 Video Lecture
| 1. What is an equation that describes number pairs? |  |
Ans. An equation that describes number pairs is a mathematical expression that shows the relationship between two numbers. It typically consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Examples of equations that describe number pairs include y = 2x + 3 and 4a - 5b = 10.
| 2. How do you solve an equation that describes number pairs? | |
Ans. To solve an equation that describes number pairs, you need to find the values of the variables that satisfy the equation. This can be done by performing various operations to isolate the variable on one side of the equation. The goal is to simplify the equation until you are left with a single variable term equal to a specific value. This value represents the solution to the equation.
| 3. What are the different types of equations that describe number pairs? | |
Ans. There are various types of equations that describe number pairs, including linear equations, quadratic equations, and exponential equations. Linear equations have a variable raised to the power of 1, quadratic equations have a variable raised to the power of 2, and exponential equations have a variable raised to a power greater than 2, typically involving an exponential function.
| 4. Can equations that describe number pairs have multiple solutions? | |
Ans. Yes, equations that describe number pairs can have multiple solutions. This means that there can be more than one set of values for the variables that satisfy the equation. For example, the equation 2x + 4 = 10 has the solution x = 3, but it also has the solution x = -1. It's important to consider all possible solutions when solving equations.
| 5. How are equations that describe number pairs used in real life? | |
Ans. Equations that describe number pairs are used in various real-life applications, such as determining the cost of items based on quantity, predicting population growth, or analyzing data trends. For example, a linear equation can be used to calculate the total cost of purchasing a certain number of items at a given price per item. Equations can also be used in physics, engineering, and economics to model real-world scenarios and make predictions.
Text Transcript from Video
- [Voiceover] Which of the
following equations is satisfied
by the five pairs of numbers
listed in the table above?
So let's look at each of these pairs,
and then let's see if we can
rule out these equations,
and then at the end, we'll
see which of these equations
can describe the relationship between
all of these pairs right over here.
So let's see, when x is
equal to negative two,
y is equal to negative three,
is that the case over here?
When x is negative two,
negative two to the third power
is negative eight,
negative eight plus three
is going to be negative five.
So, y doesn't equal negative
five, it equals negative three.
So even the first, this
point right over here,
this doesn't satisfy this first equation.
Now let's try the second one.
Three times negative two is negative six,
plus three is negative three.
So this set of points right over here,
this pair does satisfy this equation,
so we'll leave this equation
in the running for now.
Let's see, negative three
times negative two is...
negative three times
negative two is positive six,
and then you add another six to it,
you get 12, you don't get negative three,
so we're gonna rule this one out.
Let's see, negative two squared,
that's positive four, plus
six, that's positive 10,
not negative three, so
let's rule that one out.
Negative two squared is four,
minus seven is indeed negative three.
So, this equation and this equation,
for both of them, when x is equal
to negative two, y is
equal to negative three.
Now let's move down here.
When x is zero, y needs to be three.
So we have two remaining contenders.
Let's see, when x is zero,
three times zero is zero,
plus three, y is indeed equal to three.
Over here, when x is equal to zero,
we're just left with a negative seven
on the right hand side,
y equals negative seven,
so we could rule that one out.
And just like that, we
don't even have to look at
these other points, this
is the only equation
that describes the relationship between
these first two points, and we can assume
that it's going to be
true for the next three,
because we've ruled everything else out.
following equations is satisfied
by the five pairs of numbers
listed in the table above?
So let's look at each of these pairs,
and then let's see if we can
rule out these equations,
and then at the end, we'll
see which of these equations
can describe the relationship between
all of these pairs right over here.
So let's see, when x is
equal to negative two,
y is equal to negative three,
is that the case over here?
When x is negative two,
negative two to the third power
is negative eight,
negative eight plus three
is going to be negative five.
So, y doesn't equal negative
five, it equals negative three.
So even the first, this
point right over here,
this doesn't satisfy this first equation.
Now let's try the second one.
Three times negative two is negative six,
plus three is negative three.
So this set of points right over here,
this pair does satisfy this equation,
so we'll leave this equation
in the running for now.
Let's see, negative three
times negative two is...
negative three times
negative two is positive six,
and then you add another six to it,
you get 12, you don't get negative three,
so we're gonna rule this one out.
Let's see, negative two squared,
that's positive four, plus
six, that's positive 10,
not negative three, so
let's rule that one out.
Negative two squared is four,
minus seven is indeed negative three.
So, this equation and this equation,
for both of them, when x is equal
to negative two, y is
equal to negative three.
Now let's move down here.
When x is zero, y needs to be three.
So we have two remaining contenders.
Let's see, when x is zero,
three times zero is zero,
plus three, y is indeed equal to three.
Over here, when x is equal to zero,
we're just left with a negative seven
on the right hand side,
y equals negative seven,
so we could rule that one out.
And just like that, we
don't even have to look at
these other points, this
is the only equation
that describes the relationship between
these first two points, and we can assume
that it's going to be
true for the next three,
because we've ruled everything else out.
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Nov 23, 2024 Last updated |
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