Linear Algebra

There are several ways to do that. For example, you can actually graph the function. Or, you can check the ratio of the differences between the points. If this ratio (change in y, divided by change in x) is constant, the function is linear.

The quotient works out as: x^2+2x+4 and there is a remainder of -3

If: y = -2/3x+2 then the slope is -2/3 and the y intercept is 2

I is -8x^2.

You know if an equation is linear if it is a straight line. You can also know if the equation is y = mx + b where there are no absolute values nor exponents.

If you mean: 3x-4y = 19 and 3x-6y = 15

Then: x = 9 and y = 2

Because if there are two inequality eqations, you can find out which overlap if graphed.

Instead of using y = mx + b you use y (inequality sign) mx + b. By inequality sign, I mean symbols like <,>

1. Solve one equation for one of the variable. Replace the variable for the equivalent expression, in the remaining equations.2. Add one equation (possibly multiplied by some factor) to another equation, in such a way that one of the variables get eliminated.

For the specific case of linear equations, there are several additional methods, for example using determinants, or matrices.

The solution of a linear equation in two variable comprises the coordinates of all points on the straight line represented by the equation.

In general, a system of non-linear equations cannot be solved by substitutions.

It rotated the line about the point of intersection with the y-axis.

coincidental -Lines that share the same solution sets.

0

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.

That depends how the variable is combined with the other parts of the expression on each side. Here are some examples:Example 1: 2x + 5 = x - 3

Here, if you subtract "x" from both sides, you will get rid of the "x" on the right.

Example 2: x squared = 3x

Here, if you divide by "x", you get rid of the "x" on the right. However, one solution, namely x = 0, gets lost in the new equation if you do that. This is related to the fact that you should not divide by zero - and if x = 0, you are doing exactly that.

The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.

Any answers that are the same in the both tables are answers that for both equations. y=x is (1,1), 2,2), (3,3) ... y=x^2 is (1,1),(4,2)... (1,1) is in both lists.

if f(x) = 3x - 10, then whatever is put (substituted) for x in the "f(x)" bit is substituted for x in the "3x - 10" bit.

Thus f(2a) = 3(2a) - 10 = 6a - 10.

x² - 4x = 41 → x² -4x - 41 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac))/(2a)

→ x = (4 ± √(4² - 4×1×-41)/(2×1)

→ x = (4 ± √(4(4+41)))/2

→ x = (4 ± 2√45)/2

→ x = 2 ± √45

→ x = 2 + √45 (≈ 8.708) or x = 2 - √45 (≈ -4.708)

Yes, you can say something like y < infinity and y > -infinity .

With the equal sign (=).

Generally, both types of equation contain an equals sign and some combination of numbers and/or variables. That is the only thing I can think of that is common between all types of nonlinear and linear equations.