How to solve linear systems by graphing , using substitution , elimination, and graphing linear inequalities ?
My teacher is not a very good teacher , I have a test tomorrow on all these things . I asked about 13 people in my algebra class how to do it and if they could teach me , and nobody knew either , and all failed their quiz . The people that "knew" wrote it down and solved it , but their answer was wrong when I checked the back of the book . If you could explain in the simplest way possible , so I could understand , I'd be really grateful .. I'm sorry if this is a little much . me & all my friends in my class have an F or D ... examples: Solving linear systems by graphing - 1) 3x - y = -6 x + y = 2 2) y = 4x + 4 3x + 2y = 12 Solving linear systems using substitution - 1) y = 5x - 7 -4 + y = -1 2) x= y - 11 x - 3y = 1 Solving linear systems using elimination - 8x + 3y= -9 -8x + y = 29 graphing the system of linear inequalities - y < 2x + 2 y> -x - 1 if you don't know all but one of the subjects , pleasee answer anywayys . also , those ^ are examples , not asking you to solve them . I need a real explanation on how to solve it , so I can do it myself .
Describe the graph of the solution to a linear inequality in two variables?
there are 4 quadrens to a graph the one on the top rigt is quadrent I the top left is II the bottem left is III and the bottem right is IV. there is and X and Y asis to a gragh. the one going up and down is the y axis and the one left and right is X axis if you go to this page it explains more ::: http://www.purplemath.com/modules/ineqgrph.htm
Without graphing, what is the solution to the system: y=2x and y=x^2+5?
Note that when we are finding solutions, are trying to find the point at which certain particular points y and x are the same. For clarity of what is going on, will write for the first function [math]y_1=2x_1[/math] and for the second one [math]y_2=x_2^2+5[/math]The reason for this distinction is to not confuse the fact that these functions given same x will give a different output, that is the ‘y’ is not the same in both cases, though they both have a range in the complex numbers. I feel this is a distinction that should be taught in math class but notational convenience makes us stuck with the same y output for different equations.Then, we equate [math]y_1=y_2 [/math]and [math]x_1=x_2[/math]By substitution, get[math]x_2^2+5=2x_1[/math][math]x_1^1-2x_1+5=0\endnote(1)[/math]Now in general, by the distributive property,[math](x+a)(x+b)=x^2+(a+b)x+ab[/math]At first glance, this equation does not look easy to find in this form, the only factors of 5 I can think of are 5 and 1, and no combination give -2. This won’t do.We now need to employ the quadratic equation.For any equation [math]ax^2+bx+c=0[/math]where a, b, and c are constants, distinct from the equation we looked at above, we have the following…[math]x_r[/math] are the points [math]x_1[/math] and the points [math]x_2[/math] since [math]x_1=x_2[/math], where plugging in x_r to our equation at 1).[math]x_r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/math]Plugging in, get[math]x_r=1\pm2i[/math]Plugging in, get[math]y_r=2\pm4i[/math]
Graph and classify each system. Then find the solution from the graph x+3y=13 2x-y=-9?
There are three types of ways to classify linear systems: Independent and consistent (one solution) Independent and inconsistent (no solution since the two lines are parallel and share the same slope) Dependent and consistent (infinitely many solutions as the graph is of two overlapping lines) Thus you have to find the intersecting point(s) of lines x+3y=13 and 2x-y=-9 So basically, find x and y by substitution. Another way to write 2x-y=-9 is 2x+9=y. Now in the first equation substitute y with 2x+9. x+3y=13 x+3(2x+9)=13 x+6x+27=13 7x=13-27 7x=-14 x=-2 So after substituting x with -2, you should find that y is 5, so the point of intersection is (-2,5). Since there is one point of intersection, this system is independant and consistent.
Solve The Equation Using symbolic method and describe how the solution can be four on a graph or table?
5x - 28 = -3 add 28 to both sides of the equal sign 5x - 28 + 28 = -3 + 28 5x = 25 divide both sides by 5 5x/5 = 25/5 x = 5 10 - 3x = 7x - 10 We need the variable terms on one side of the equal sign and the constants on the other side. Of the two variables terms, 3x is smaller than 7x. Therefore, to transfer the 3x to the same side as the 7x, add 3x to both sides of the equal sign 10 - 3x + 3x = 7x - 10 + 3x 10 = 10x - 10 To isolate the x term, add 10 to both sides 10 + 10 = 10x - 10 + 10 20 = 10x divide both sides by 10 20/10 = 10x/10 2 = x
How can I find the solution of a system of linear equation using its graph?
The solution to a system of 2 linear equations has 0,1 or an infinite number of solutions. If the equations are represented as two lines the solution(s) are where the lines cross. In the case of parallel lines they never cross and thus there are no solutions. If the two lines are coincidental then they are “on top” of each other and thus have an infinite number of solutions. The only other choice is that they cross at one point in which case that point of crossing is the solution. In this case x = 1 and y = 3.
How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?
here is the best website that can answer this MAT 116 Week 7 DQ 1 (Version 2) - Take My Online Math Classand one of the answers is below There can be three solution sets of linear equalities. They can have one solution, or they can have no solutions or they can have infinitely many solutions. System of linear inequalities that have many or infinite solutions are called ” dependent”. So, the solution to the system of linear inequalities means graphing each individual inequality, and then finding the overlapping regions. Yes, when there is overlapping, the solution to system of linear inequalities will satisfy both inequalities. When there is no overlapping in shaded regions, there will be no solution to system of linear inequalities. Comment: Talking of linear inequalities (which are basically extensions of linear equations), one can use them to compare Fahrenheit and Celsius temperature scales, different phone rates, money exchange rates, and to figure out distance & speed. Do I take the shorter route where I have to go at this speed or the longer router where the speed limit is higher. y < 7, x – y < 9, y > 3 are examples of linear inequalities (and not linear equations). If there is a symbol < or > or < or > then the expression has to be an inequality. In case an expression has = sign, then the expression becomes an equation.
System of equations that describes the stiuation?
Let x represent the amount of 22% acid used in the final solution (in ml) and x represent the amount of 8% acid used in the final solution (in ml) We know x + y = 101 0.22x + 0.08y = 0.12(x + y) Let's continue the second equation and solve for x 0.22x + 0.08y = 0.12x + 0.12 y 0.22x - 0.12x = 0.12 y - 0.08y 0.1x = 0.04y x = 0.04y / 0.1 x = 0.4y Now plug x into the first equation x + y = 101 0.4y + y = 101 1.4y = 101 y = 72.14 ml x = 0.4y x = 0.4(72.14) x = 28.86 ml I hope this helped Kia