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How many solutions does an inconsistent equation have?
An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.
How do you know if a solution is always true or sometimes true?
We call a solution any value of the variable which satisfies the given equation. If the number of values you get (which always satisfy the equation) is a finite number, then the equation is sometimes true (meaning it is true only for those values you got). ex. x + 3 = 5 is true only when x is 2. x2 - 5 = 4 is true only when x is -3 or 3. √x = 7 is true only when x is 49. (check:) 2(3x - 1) = 6x - 2 is always true, meaning for any value that x can take on, both sides becomes equal when x is replaced by it. 2(3x - 1) = 6x - 26x - 2 = 6x - 2 (both sides seems to be equal) , or subtract 6x and add 2 to both sides 0 = 0 a true statement. Since 0 = 0 is an equivalent statement to the original equation and it is a true one, then the original equation must be also a true statement. Thus, there are infinitely many solutions for the given equation. Therefore, the given equation is always true. Sometimes, before you start to solve an equation, you need to exclude some value(s) for the variable of being a solution, because they can make the equation undefined. For example, if the variable happens to be in the denominator, you have to exclude all the values of the variable that make the denominator equal to zero.
What do you call a number that stands alone in an equation?
You can call it a "number." To distinguish it from a variable expression, you can also call it a "constant."
What is the general equation of the straight line?
A straight line will have a constant gradiant, so its change in height over time will be some multiple of x. We'll call this bx. The other point of consideration is where the line crosses the y axis (x=0). We'll call this point a. So the equation of a straight line can be given as y=a+bx
How do you find the equation of the line given the slope equals 5 and the x intercept equals 7?
Call the intercept with the y-axis b. The equation for the line is then y=5x+b With the information about the x-intercept we get: 0=5*7+b b=-35
