System of linear equations
Okay, so you know how sometimes you have two or more things that are related to each other, kind of like how your age is related to how many birthdays you've had? That's kind of what a system of linear equations is like!
In a system of linear equations, we have two or more things that are related to each other. These things are called variables, and they usually involve numbers. So let's pretend we're trying to figure out how many apples and oranges our mom bought at the grocery store. We can use a system of linear equations to figure it out!
We can use the letter "a" to represent the number of apples, and "o" to represent the number of oranges. Let's say we know that we have a total of 10 fruits, so we can write our first equation as:
a + o = 10
This means that the number of apples plus the number of oranges equals 10. But we still need more information to figure out how many of each fruit there are.
Let's say our mom spent $6 on the fruits. We know that apples cost $1 each, and oranges cost $2 each. We can use this information to create another equation:
1a + 2o = 6
This equation means that if we multiply the number of apples by $1 and the number of oranges by $2, we get a total of $6.
Now we have two equations:
a + o = 10
1a + 2o = 6
These equations make up our system of linear equations!
To solve this system, we need to find the values of "a" and "o" that make both equations true. We can use different methods to do this, but one common way is to use substitution.
Let's start by solving the first equation for "a":
a + o = 10
a = 10 - o
Now we can substitute this expression for "a" into the second equation:
1a + 2o = 6
1(10 - o) + 2o = 6
Simplifying this equation gives us:
10 - o + 2o = 6
10 + o = 6
o = 6 - 10
o = -4
Uh oh, it looks like we have a problem! How can we have negative oranges? This means that our system of equations doesn't have a solution, which means there's no way to figure out how many apples and oranges our mom bought that satisfies both equations.
But don't worry, sometimes systems of linear equations do have solutions! They can be used to solve all sorts of problems, like figuring out how much gas you need to buy for a road trip or how much time it will take to finish your homework. It's like a big puzzle that involves using math to solve real-life problems!
In a system of linear equations, we have two or more things that are related to each other. These things are called variables, and they usually involve numbers. So let's pretend we're trying to figure out how many apples and oranges our mom bought at the grocery store. We can use a system of linear equations to figure it out!
We can use the letter "a" to represent the number of apples, and "o" to represent the number of oranges. Let's say we know that we have a total of 10 fruits, so we can write our first equation as:
a + o = 10
This means that the number of apples plus the number of oranges equals 10. But we still need more information to figure out how many of each fruit there are.
Let's say our mom spent $6 on the fruits. We know that apples cost $1 each, and oranges cost $2 each. We can use this information to create another equation:
1a + 2o = 6
This equation means that if we multiply the number of apples by $1 and the number of oranges by $2, we get a total of $6.
Now we have two equations:
a + o = 10
1a + 2o = 6
These equations make up our system of linear equations!
To solve this system, we need to find the values of "a" and "o" that make both equations true. We can use different methods to do this, but one common way is to use substitution.
Let's start by solving the first equation for "a":
a + o = 10
a = 10 - o
Now we can substitute this expression for "a" into the second equation:
1a + 2o = 6
1(10 - o) + 2o = 6
Simplifying this equation gives us:
10 - o + 2o = 6
10 + o = 6
o = 6 - 10
o = -4
Uh oh, it looks like we have a problem! How can we have negative oranges? This means that our system of equations doesn't have a solution, which means there's no way to figure out how many apples and oranges our mom bought that satisfies both equations.
But don't worry, sometimes systems of linear equations do have solutions! They can be used to solve all sorts of problems, like figuring out how much gas you need to buy for a road trip or how much time it will take to finish your homework. It's like a big puzzle that involves using math to solve real-life problems!
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