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You can solve a system of equations using a few methods: elemination and subsitution.
In the elemination method you would multiply each of your equations by a factor that would cause one of the variables to be eleminated.
ex: If you had 2x-3y=5 and 3x+6y=4 you would multiply the first equation by a factor of 2 (distributing the 2 to each term), giving you a new equation of 4x-6y=10. Now your y terms would cancel. You line up the equations like:
3x+6y=4
4x-6y=10 you simply cancel the y terms and add the others giving you:
7x=14 you then solve for x (in this case divide by 7)
x=2
now you plug in x=2 into one of the first equations and solve
3x+6y=4
3(2)+6y=4 plug in x
6+6y=4 multiply
6y=-2 add like terms
y=-1/3 solve for y
To solve using the subsitution method you would take an equation and solve for one variable then plug that into the other equation.
ex. (using the same equations as before)
2x-3y=5
2x=3y+5
x=(3/2)y+(5/2)
3x+6y=4
3((3/2)y+(5/2))+6y=4 plug in for x
(9/2)y+(15/2)+6y=4 distribute the 3
(21/2)y=(-7/2) add like terms
y=(-1/3) solve for y
you would then plug in y and solve for x
2x-3(-1/3)=5
2x+1=5
2x=4
x=2
Hope this helps!
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Solve the following system of equations using sustitution x6y-4 x-2y 28?
To solve a system of equations, you need equations (number phrases with equal signs).
How can you solve a system of equations?
The answer depends on whether they are linear, non-linear, differential or other types of equations.
How does writing equivalent equations help you solve a system of equations?
You can write an equivalent equation from a selected equation in the system of equations to isolate a variable. You can then take that variable and substitute it into the other equations. Then you will have a system of equations with one less equation and one less variable and it will be simpler to solve.
Use the substitution method to solve the system of equations Enter your answer as an ordered pair?
Use the substitution method to solve the system of equations. Enter your answer as an ordered pair.y = 2x + 5 x = 1
How would you know if a linear system has a solution?
One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent. If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent. If the graph of the equations is the same line, the system has infinitely simultaneous solutions. We can use several methods in order to solve the system algebraically. In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example, 2x + 3y = 6 4y + 6y = 12 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. Try to solve this system of equations, 2x + 3y = 6 4x + 6y = 7 If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations). When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
Solve the following system of equations using sustitution x6y-4 x-2y 28?
To solve a system of equations, you need equations (number phrases with equal signs).
How can you solve a system of equations?
The answer depends on whether they are linear, non-linear, differential or other types of equations.
How does writing equivalent equations help you solve a system of equations?
You can write an equivalent equation from a selected equation in the system of equations to isolate a variable. You can then take that variable and substitute it into the other equations. Then you will have a system of equations with one less equation and one less variable and it will be simpler to solve.
Translate this word problem as a system of equations and then solve using substitution?
A system of equations is two or more equations that share at least one variable. Once you have determined your equations, solve for one of the variables and substitute in that solution to the other equation.
How do you solve 3 dimensional equations?
You can solve the system of equations with three variables using the substitute method, or using matrix operations.
How do you solve systems of equation algebraically?
There are 5 ways to solve a system. The most popular is to write both in standard notation then add the equations together. The easiest to explain is to use substitution. Solve one for one of the variables then substitute in the other equation. The other ways to solve are to use graphing and find the intersection. Determinants and matrices are the other two ways.
What it means to be a solution to a linear system algebraically?
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
Is there one method to solve a system of equations?
No, there are several methods.
To solve a three variable system of equations you can use a combination of the elimination and substitution methods?
True. To solve a three variable system of equations you can use a combination of the elimination and substitution methods.
Use the substitution method to solve the system of equations Enter your answer as an ordered pair?
Use the substitution method to solve the system of equations. Enter your answer as an ordered pair.y = 2x + 5 x = 1
When using the substitution method to solve a nonlinear system of equations you should first see if you can one variable in one of the equations in the system?
isolate
Solve the system of equations Enter your answer as an ordered pair?
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