SOLUTION: PLS HELP.ME ANSWER THIS PLS.. Simplify the following Linear Equation. Using Elimination,Substition,Determinants and Graphical. 1) 2x+3y=18 4x+6y=12 2) 4x+y=6

Question 992474: PLS HELP.ME ANSWER THIS PLS..
Simplify the following Linear Equation.
Using Elimination,Substition,Determinants and Graphical.
1) 2x+3y=18
4x+6y=12
2) 4x+y=6
-8x-2y=21

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Using:

1)

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition

Lets start with the given system of linear equations

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 2 and 4 to some equal number, we could try to get them to the LCM.

Since the LCM of 2 and 4 is 4, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this:

Multiply the top equation (both sides) by 2
Multiply the bottom equation (both sides) by -1

So after multiplying we get this:

Notice how 4 and -4 and 36 and -6 add to zero (ie )

However 36 and -12 add to 24 (ie );

So we're left with

which means no value of x or y value will satisfy the system of equations. So there are no solutions

So this system is inconsistent

2)

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition

Lets start with the given system of linear equations

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 4 and -8 to some equal number, we could try to get them to the LCM.

Since the LCM of 4 and -8 is -8, we need to multiply both sides of the top equation by -2 and multiply both sides of the bottom equation by -1 like this:

Multiply the top equation (both sides) by -2
Multiply the bottom equation (both sides) by -1

So after multiplying we get this:

Notice how -8 and 8 and -12 and 2 add to zero (ie )

However -12 and -21 add to -33 (ie );

So we're left with

which means no value of x or y value will satisfy the system of equations. So there are no solutions

So this system is inconsistent

1)

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
We'll use substitution. After moving 3*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=24=0. Since , x=-27.

Answer: .

2)

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
We'll use substitution. After moving 1*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=-33=0. Since , x=9.75.

Answer: .

1)

by systems of linear equations are of the form

and where is the coefficient determinant given by .
in your case ,,,,,and
then you have:
determinant =>=>=>
since determinant equal to zero, this system has no solution

2)

in this case ,,,,,and
then you have:
determinant =>=>=>
=>
so, determinant equal to zero, this system has no solution

1)

Solved by pluggable solver: Solve the System of Equations by Graphing

Start with the given system of equations:

In order to graph these equations, we need to solve for y for each equation.

So let's solve for y on the first equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.

2)

Solved by pluggable solver: Solve the System of Equations by Graphing

Start with the given system of equations:

In order to graph these equations, we need to solve for y for each equation.

So let's solve for y on the first equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Add to both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.

Answer by ikleyn(52832) (Show Source): You can put this solution on YOUR website!
.
1)
.

Divide the second equation by 2. You will get

.

Now compare two equations in this system. They have the same left parts and different right parts.

Hence, the system is inconsistent. You need not to make long calculations. You can establish it in couple lines.

2) The same approach works for the second system, too.

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