Check by substituting whether x = -3 and y= -3 is a solution of 3(x-1) -2y = 4. Find one more solution. How many
more solutions can you find?
Answers
Answer:
Non-Linear Systems
In this lesson we will be specifically looking at systems of nonlinear equations that have two equations and two unknowns. We will look at
solving them two different ways: by the substitution method and by the elimination by addition method. These methods will be done in the same manner that they are done with systems of linear equations, we will just be applying it to nonlinear systems.
Using substitution, elimination and graphing, you will be asked to determine the solution set between 2 parabolas, a parabola and a line, a circle
and a parabola, etc. The number of solutions in the consistent-independent system can be 0 to 4 in non-linear systems. For example a circle and
a parabola can have 4 solutions. Therefore sketching a graph of the system before you solve it will be helpful in determining how many solutions to look for. Also, checking your solutions is a very important exercise in this section.
System of Nonlinear Equations
A system of nonlinear equations is two or more equations, at least one of which is not a linear equation, that are being solved simultaneously.
Note that in a nonlinear system, one of your equations can be linear, just not all of them.
Example 1: Solve the system of equations by the substitution method:
Solving the first equation for y we get:
Substitute the expression 3x + 2 for y into the second equation and solve for x:
Plug in -1/2 for x into the equation y = 3x + 2 to find y’s value
(-1/2, 1/2) is one solution to this system.
Plug in 2 for x into the equation y = 3x + 2 to find y’s value.
(2, 8) is another solution to this system.
You will find that if you plug either the ordered pair (-1/2, 1/2) OR (2, 8) into BOTH equations of the original system, that they
are both a solution to BOTH of them.
(-1/2, 1/2) and (2, 8) are both a solution to our system.
Example 2: Solve the system of equation by the elimination method:
The variable that you want to eliminate must be a like variable. In other words, it must not only be the same variable, but
have the same exponent. Note how x is squared on both equations. So we would be able to get opposite coefficients on them
and then when we added the two equations together they would drop out.
Note how y is to the one power in the first equation and squared on the second equation. If we would pick y to eliminate we would
have a problem because we cannot combine unlike terms together. y squared -y would be y squared - y NOT 0.
So I proposed that we multiply the second equation by -1, this would create a 1 and a -1 in front of the x squareds and we will
have our opposites.
Multiplying the second equation by -1 we get:
Add the equations:
Solve for y:
Solve for x. You can choose any equation used in this problem to plug in the found y values.
I choose to plug in -4 for y into the first equation to find x’s value.
So (0, - 4) is one solution to this system.
Now plug in 2 for y into the first equation to find x’s values.
So and are two more solutions to this system.
You will find that if you plug the ordered pairs (0, - 4), , and into BOTH equations of the original system, that
they would all be solutions to BOTH of them.
(0, - 4), , and are all solutions to our system.
Answer:
Thankyou for free points
Answer:
Thankyou for free points