solve these problems

Question

x+y=11

y=2x-1

what type of system is this?

Answer 1

As you may know there are three types of systems: inconsistent, dependent and independent. 

Inconsistent means that there is no solution in the form of x= that satisfied both of the equation, meaning there's no x value for which both equation equal each other.

Dependent is when the two equations are actually the same, meaning if we draw them on a graph we will see that they are one and the same line. 

Independent is when the two equations have one point of intersection. 

So let's rearrange these two equations so that both are in the y= form. 

x+y=11 -> y=11-x

y=2x-1

Now what we must do is equal the two equations to each other. The reason we can do this is because they are both equal to y (transitive relation). 

11-x=2x-1. Solve for x.

10-x=2x

10=3x

10/3=x

So both of these systems are equal at one point where x=10/3 so therefore these systems are independent. 

Hope this helped!

Answer 2

Hi, Ellen.

This is a system of linear equations; you can tell because the variables have an exponent of 1 (which you don't have to write).

When we solve a system of equations, we find the solution for one of the variables, then use that value to find the others. This solution will have two parts, for x and y.

There are 2 popular methods of solving systems of equations, substitution and elimination. Substitution would work well for this case, because the 2nd equation already has one variable by itself. Since y equals 2x-1, we can substitute 2x-1 in for y in the first equation, and solve for x:

x + (2x - 1) = 11

x + 2x - 1 = 11

3x - 1 = 11
   + 1    + 1
  3x = 12

3x = 12
 3      3

x = 4

We can now use 4 in place of x in either equation to find y:

4 + y = 11

y = 7

The solution set is (4,7). We can substitute those values into the 2nd equation to check:

7 = 2(4) - 1

7 = 8 - 1

It works, so the solution is (4,7).

Answer 3

Hello Ellen,

This is system of equations with two variables. In this we solve for the value of the variables x and y. There are different ways to solve this. We'll use substitution method to solve this.

From the first equation ( x + y = 11) we'll find the value of x. Subtract y from both sides.

x + y - y = 11 - y

You'll get x = 11 - y

Now, substitute the value of x in the second equation ( y = 2x - 1) you'll get

y = 2(11 - y) - 1

Solve for y

y = 22 - 2y - 1

Add 2y on both sides of equation, you'll get

y + 2y = 22 - 2y + 2y - 1

3y = 21

divide both sides by 3

(3/3)y = 21/3

y = 7

Now, sustitute the value of y in first equation(x + y = 11) and solve for x.

x + 7 = 11

Subtract 7 from both sides of the equation

x + 7 - 7 = 11 - 7

x = 4

Finally your answers are x = 4 and y = 7.

I hope this works out for you.