How do you write a system of linear equations in two variables?
Explain this in words and by using mathematical notation in an equation.
What steps will be taken to solve the system that you provided?
any explanation given here will look remarkably like whatever is in your text, or you can find using google or wolframalpha.
If you have a particular problem, come back with a more specific question.
If you know what a linear equation is, a system is just a set of equations. You can use as many variables as you like.
There are various methods of solving such systems. Read up on them.
To write a system of linear equations in two variables, you need to have two different linear equations involving the same two variables. Let's say the two variables are x and y. Each equation can be expressed in the form of ax + by = c, where a, b, and c are constants.
For example, let's write a system of linear equations:
Equation 1: 2x + 3y = 7
Equation 2: 4x - y = 5
To solve this system, follow these steps:
Step 1: Pick one of the equations and solve it for one variable in terms of the other variable. In this case, let's solve Equation 2 for y:
4x - y = 5
y = 4x - 5
Step 2: Substitute the expression you found for y back into the other equation. Using Equation 1, substitute y with 4x - 5:
2x + 3(4x - 5) = 7
Step 3: Simplify and solve for x:
2x + 12x - 15 = 7
14x - 15 = 7
14x = 22
x = 22/14
x = 11/7 or approximately 1.57
Step 4: Substitute the value of x back into one of the equations to solve for y. Using Equation 1:
2(11/7) + 3y = 7
22/7 + 3y = 7
3y = 49/7 - 22/7
3y = 27/7
y = 9/7 or approximately 1.29
So, the solution to the system of linear equations is x = 11/7 and y = 9/7.
To write a system of linear equations in two variables, you need two linear equations that involve the same two variables. Let's say these variables are x and y.
In mathematical notation, a system of linear equations can be represented as follows:
Equation 1: ax + by = c
Equation 2: dx + ey = f
Where:
a, b, c, d, e, and f are coefficients or constants
x and y are the variables you are solving for
To solve the system of linear equations, you can follow these steps:
1. Rearrange each equation so that the variables (x and y) are on one side and constants (coefficients and the term on the right side of the equation) are on the other side.
2. Once you have both equations in this form, set them equal to each other. This equals sign ( = ) represents the fact that both sides of the equations are equal. For example:
ax + by = c --> Equation 1
dx + ey = f --> Equation 2
This can be represented as:
ax + by = dx + ey
3. Now, simplify the equation by collecting like terms. Group terms with x together and terms with y together. This will give you the standard form of the system of linear equations:
(ax - dx) + (by - ey) = 0
4. Factor out the common variables and divide both sides by the coefficient of x and y. This will give you the simplified form of the system of linear equations:
(x(a-d) + y(b-e)) = 0
5. Finally, set the expression inside the parentheses equal to zero:
x(a-d) + y(b-e) = 0
This is the general form of a system of linear equations in two variables.
To solve the system, you can use various methods such as substitution, elimination, or matrix methods. Each method involves manipulating the equations to either eliminate one variable or solve for one variable in terms of the other. By finding the values of x and y that satisfy both equations, you will have solved the system of linear equations.