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If you were to solve the following system by substitution what would be the best variable to solve for and from what equation 2x plus 6y equals 9 3x-12y equals 15?
2x + 6y = 93x - 12y = 15Chose the second equation because you can simplify it.3x - 12y = 15 divide by 3 to both sidesx - 4y = 5 add 4y to both sidesx = 4y + 5Replace 4y + 5 for x to the first equation.2x + 6y = 92(4y + 5) + 6y = 98y + 10 + 6y = 914y = -1y = -1/14x = 4y + 5x = 4(-1/14) + 5x = -2/7 + 5x = -2/7 + 35/7x = 33/7
What must be true about the lines of a system of equation that has not one solution but infinitely many solutions?
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
What is the solution to this system of equations y equals -3x-2?
-1
A system of linear equations with an infinite number of solutions?
This can happen in different ways: a) More variables than equations. For instance, a single equation with two variables (such as x + y = 15), two equations with three variables, two equations with four variables, etc. b) To of the equations describe the same line, plane, or hyper-plane - this, in turn, will result in that you "really" have less equations than it seems. For example: y = 2x + 3 2y = 4x + 6 The second equation is simply the first equation multiplied by 2.
Solve the following system of equations using substitutions 2x plus 3y equals -1 and 5x-2y equals -12?
First get y in terms of x: 5x-2y=-12 ----- -2y=-12-5x ------ y=6+(5/2)x Sub into other equation: 2x+3y=-1 ---- 2x+3(6+(5/2)x)=-1 Solving for x gets: x= -2 Sub into other equation: 5x-2y= -12 --- 5(-2)-2y= -12 --- y=1 So x= -2, and y= 1
What is usually the second step when solving a system of nonlinear equations by substitution?
The second step when solving a system of nonlinear equations by substitution is to solve one of the equations for one variable in terms of the other variable(s). Once you have expressed one variable as a function of the other, you can substitute that expression into the other equation to create a single equation in one variable. This allows for easier solving of the system.
What is usually the first step in solving a system of equation by substitution?
The first step is to solve one of the equations for one of the variables. This is then substituted into the other equation or equations.
What is most likely to be the first step in solving a system of nonlinear equations by substitution?
The first step in solving a system of nonlinear equations by substitution is to isolate one variable in one of the equations. This involves rearranging the equation to express one variable in terms of the other(s). Once you have this expression, you can substitute it into the other equation(s) in the system, allowing you to solve for the remaining variables.
How do use substitution when solving system of equations?
You use substitution when you can solve for one variable in terms of the others. By substituting, you remove one variable from the equation, which can then be solved. Once you solve for one variable, you can use substitution to find the other.
Can solve a system of linear equation by substitution?
Yes, a system of linear equations can be solved by substitution. This method involves solving one of the equations for one variable and then substituting that expression into the other equation. This process reduces the system to a single equation with one variable, which can then be solved. Once the value of one variable is found, it can be substituted back to find the other variable.
How do you solve the system of equation by substitution x plus 2y-2 3x plus 4y6?
If you mean x+2y = -2 and 3x+4y = 6 then by solving the simultaneous equations by substitution x = 10 and y = -6
How do you find system of linear equation in two variable?
By elimination and substitution
What are the advantages and disadvantages of solving a system of equations by substitution?
The substitution method for solving a system of equations is advantageous because it can be straightforward, especially when one equation is easily solvable for one variable, allowing for direct substitution. It can also provide clear insights into the relationships between variables. However, its disadvantages include the potential for increased complexity when dealing with more variables or complicated equations, and it may be less efficient than other methods, like elimination, for larger systems. Additionally, if the equations are not easily manipulated, it can lead to errors in calculation.
What is usually the first step in solving a system of nonlinear equations by substitution?
The first step is usually to solve one of the equations for one of the variables.Once you have done this, you can replace the right side of this equation for the variable, in one of the other equations.
Which situation may cause someone to use substitution in order to solve a system of equations?
Substitution is often used when one of the equations in a system is already solved for one variable, or can be easily manipulated to do so. For example, if you have the equations (y = 2x + 3) and (3x + 2y = 12), substituting the expression for (y) from the first equation into the second allows for straightforward solving. This method is particularly useful when dealing with linear equations, as it simplifies the process of finding the variable values.
What is the first step in solving the following system of equations by substitution?
The first step is to show the equations which have not been shown.
Which is most likely the first step in solving a system of nonlinear equations by substitution APEX?
Isolating a variable in one of the equations.
