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Solving Linear Equations with Variable on Both Sides
By yourteachermathhelp
This video describes the process of solving a linear equation with the variable on both sides of the equation (5c + 15 = 2c - 12). The instructor walks through a very good description of the process showing all steps. The equation is finally put into y=mx+b form.
One-step equations with multiplication and division
By Khan Academy
Let's get a conceptual understanding of why one needs to divide both sides of an equation to solve for a variable.
One-step equations with multiplication and division
By Khan Academy
Let's get a conceptual understanding of why one needs to divide both sides of an equation to solve for a variable.
Solving Quadratic Equations by Factoring - MathHelp.com
By yourteachermathhelp
This video is a clip of a smaller segment. Students learn to solve quadratic equations by the method of their choice, using the following rules. If possible, use the factoring method. If there is no coefficient on the squared term, and the middle term of the trinomial is even, use completing the square. If there is a coefficient on the squared term, and/or if the middle term is odd, use the quadratic formula. If the variable only appears in the squared term, get the variable by itself on one side of the equation and square root both sides.
Linear Equations in Two Variables
By Meritnation
YouTube presents Linear Equations in Two Variables, an educational video resource on math.
Adding and Subtracting Polynomials | MathHelp.com
By MathHelp.com
In this example, notice that each of our variables, x, y, and z, appears in all three equations. To solve this system, we use the addition method. In other words, let’s start with our first two equations, x + y + z = 4, and x – y + z = 2. Notice that if we add these equations together, the +y and –y will cancel out, and we have 2x + 2z = 6. So, in our new equation, 2x + 2z = 6, we’ve eliminated the variable y. Unfortunately, we still haven’t solved for any of our variables. However, if we can create another equation with just x and z in it, then we’ll have a system of equations in two variables, which we can use to solve for x and z. To create another equation with just x and z in it, we need to eliminate y. We can’t add the first and second equations together, because we’ve already done that. However, notice that if we add the first and third equations together, the first equation has a +y and the third equation has a –y, so we’ll be able to eliminate the y. So we have our first equation, x + y + z = 4, and our third equation, x – y – z = 0, and adding them together, notice that the +y – y cancels out, and, as a bonus, the +z – z also cancels out, so we have 2x = 4, and dividing both sides by 2, x = 2. Now, since we know that x = 2, notice that if we plug a 2 in for x in the equation that we created earlier, we can solve for z. And we have 2(2) + 2z = 6, or 4 + 2z = 6, and subtracting 4 from both sides, we have 2z = 2, and dividing both sides by 2, z = 1. So x = 2 and z = 1, and to find the value of y, we simply plug our values of x and z into any of the equations in the original system. Let’s use the first equation, x + y + z = 4. Since x = 2 and z = 1, we plug a 2 in for x and a 1 in for z, and we have 2 + y + 1 = 4, or 3 + y = 4, and subtracting 3 from both sides, y = 1. So x = 2, y = 1, and z = 1, and finally, we write our answer as the ordered triple, x, y, z, or (2, 1, 1).
Solving systems of equations in three variables
By MathPlanetVideos
Solve the systems of equation in our example.
Solving systems of equations in two variables
By MathPlanetVideos
Solve the system of equations: {2x−4y=0 −4x+4y=−4
Systems of Three Equations | MathHelp.com
By MathHelp.com
Here we’re asked to graph the following function and use the horizontal line test to determine if it has an inverse. And if so, find the inverse function and graph it. So let’s start by graphing the given function, f(x) = 2x – 4, and remember that f(x) is the same as y, so we can rewrite the function as y = 2x – 4. Now, we simply graph the line y = 2x – 4, which has a y-intercept of -4, and a slope of 2, or 2/1, so we go up 2 and over 1, plot a second point and graph our line, which we’ll call f(x). Next, we’re asked to use the horizontal line test to determine if the function has an inverse. Since there’s no way to draw a horizontal line that intersects more than one point on the function, the function does have an inverse. So we need to find the inverse and graph it. To find the inverse, we switch the x and the y in original function, y = 2x – 4, to get x = 2y – 4. Next, we solve for y, so we add 4 to both sides to get x + 4 = 2y, and divide both sides by 2 to get 1/2x + 2 = y. Next, let’s flip our equation so that y is on the left side, and we have y = 1/2x + 2. Finally, we replace y with the notation that we use for the inverse function of f, as shown here. And remember that we’re asked to graph the inverse as well, so we graph y = ½ x + 2. Our y-intercept is positive 2, and our slope is ½, so we go up one and over 2, plot a second point, graph the line, and label it as the inverse function of f. Notice that the graph of the inverse function is a reflection of the original function in the line y = x.
Equations with variables on both sides
By Khan Academy
Sal solves the equation 2x + 3 = 5x - 2.������������