Solving Equations - Algebra 2

Add 12 on both sides.

Add on both sides of the equation.

Simplify both sides.

Divide by 13 on both sides.

The answer is:

Add on both sides.

The equation becomes:

Add nine on both sides.

The equation becomes:

Divide by 16 on both sides.

Reduce the fractions.

The answer is:

Determine the least common denominator of the fractions by multiplying all the denominators together.

We can multiply both sides by 84 in order to eliminate the fractions.

Simplify both sides.

Add 21 on both sides.

Divide by 28 on both sides.

The answer is:

Add 34 on both sides of the equation.

The equation becomes:

Divide by eight on both sides.

The answer is:

Distribute the x through the parentheses:

x2 –2x = x2 – 8

Subtract x2 from both sides:

–2x = –8

Divide both sides by –2:

x = 4

Given the equation,

and

Plug in for to the equation,

Solve and simplify.

Multiply both sides by 3:

Distribute:

Subtract from both sides:

Add the terms together, and subtract from both sides:

Divide both sides by :

Simplify:

Plug in the value for .

Simplify

Subtract

On the equation, replace x with 2 and then simplify.

Equation 1:

Equation 2:

Equation 3:

Adding the terms of the first and second equations together will yield .

Then, add that to the third equation so that the y and z terms are eliminated. You will get .

This tells us that x = 1. Plug this x = 1 back into the systems of equations.

Now, we can do the rest of the problem by using the substitution method. We'll take the third equation and use it to solve for y.

Plug this y-equation into the first equation (or second equation; it doesn't matter) to solve for z.

We can use this z value to find y

So the solution set is x = 1, y = 2, and z = –5/3.

rearranges to

and

, so

To solve this problem we can first add to each side of the equation yielding

Then we take the square root of both sides to get

Then we calculate the square root of which is .

In the second equation, you can substitute for from the first.

Now, substitute 2 for in the first equation:

The solution is

Isolate in the first equation.

Plug into the second equation to solve for .

Plug into the first equation to solve for .

Now we have both the and values and can express them as a point: .

Add the equations together.

Put the terms together to see that .

Substitute this value into one of the original equaitons and solve for .

Now we know that , thus we can find the sum of and .

To find the point where these two lines intersect, set the equations equal to each other, such that is substituted with the side of the second equation. Solving this new equation for will give the -coordinate of the point of intersection.

Subtract from both sides.

Divide both sides by 2.

Now substitute into either equation to find the -coordinate of the point of intersection.

With both coordinates, we know the point of intersection is . One can plug in for and for in both equations to verify that this is correct.

To solve for , you must isolate it from the other variables. Start by adding to both sides to give you . Now, you need only to divide from both sides to completely isolate . This gives you a solution of .

First, you must multiply the left side of the equation using the distributive property.

This gives you .

Next, subtract from both sides to get .

Then, divide both sides by to get .

Combine like terms on the left side of the equation:

Use the distributive property to simplify the right side of the equation:

Next, move the 's to one side and the integers to the other side: