12a + 8b....common factor is 4
4(3a + 2b) <==
1. Understand what multi-variable equations are.
Two or more linear equations that are grouped together are called a system. That means that a system of linear equations is when two or more linear equations are being solved at the same time.
[1] For example:
• 8x - 3y = -3
• 5x - 2y = -1
These are two linear equations that you must solve at the same time, meaning you must use both equations to solve both equations.
2. Know that you are trying to figure out the values of the variables, or unknowns.
The answer to the linear equations problem is an ordered pair of numbers that make both of the equations true.
In the case of our example, you are trying to find out what numbers ‘x’ and ‘y’ represent that will make both of the equations true.
• In the case of this example, x = -3 and y = -7. Plug them in. 8(-3) - 3(-7) = -3. This is TRUE. 5(-3) -2(-7) = -1. This is also TRUE.
3. Know what a numerical coefficient is.
The numerical coefficient is simply the number that comes before a variable.[2] You will use these numerical coefficients when using the elimination method. In our example equations, the numerical coefficients are:
• 8 and 3 for the first equation; 5 and 2 for the second equation.
4. Understand the difference between solving with elimination and solving with substitution.
When you use elimination to solve a multivariable linear equation, you get rid of one of the variables you are working with (such as ‘x’) so that you can solve the other variable (‘y’). Once you find ‘y’, you can plug it into the equation and solve for ‘x’ (don’t worry, this will be covered in detail in Method 2).
• Substitution, on the other hand, is where you begin working with only one equation so that you can again solve for one variable. Once you solve one equation, you can plug in your findings to the other equation, effectively making one large equation out of your two smaller ones. Again, don’t worry—this will be covered in detail in Method 3.
5. Understand that there can be linear equations that have three or more variables.
Solving for three variables can actually be done in the same way that equations with two variables are solved. You can use elimination and substitution, they will just take a little longer than solving for two, but are the same process.
Answer:
(0,0)
Step-by-step explanation:
Answer:
b) Circle
Step-by-step explanation:
<em>All</em> of the conic sections have vertices and foci. These features are not usually talked about for a circle, so perhaps "circle" is the expected answer.
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A circle is a special case of ellipse with eccentricity 0. Its foci are coincident at its center, and its vertices are the ends of any pair of perpendicular diameters.
Answer:
The correct option is;
The function will intersect at x = -2 and x = 1
Step-by-step explanation:
The question parameters are
The functions in the question are f(x) and g(x)
The solution to the equation f(x) = g(x) are -2, and 1
Given that the equations, f(x) and g(x), are both given in values of x, their solution will be the x values that satisfies both functions
Therefore, the functions will intersect (have the same values of f(x) and g(x)) at the points of the solutions, which are given as x = -2, and x = 1
