Tutor profile: Mark D.
You have two different equations in the system of equations below. Use substitution to solve for the given system. Find x and y. 2*x + y = -10 8*y - 8 = x
First you want both equations to look to same. To do this, we're going to manipulate one of the equations to match the format of the other. In this example, we'll be manipulating the 2nd equation. To do this we will add 8 to both sides of the equation and subtract x from both sides. Now, we have -x + 8*y = 8. Next, we will write each equation over top of one another like this: 2*x + y = -10 -x + 8*y =8 Then, you want to solve for y in the top equation. This gives you -10 - 2*x = y. Now, we can plug in -10 - 2*x for y in the second equation, and it will look like -x + 8( -10 - 2*x) = 8. Now, we can solve for x because it's a one variable equation. x = (88/-17). Now, we plug the x value in for the first equation and we solve for y. So, y = (-6/17).
A triangle has a width of 3 and a height of 5. Find the hypotenuse of the triangle.
First, we write down our known values and draw and appropriate triangle. Then, we use the Pythagorean Theorem to solve for the hypotenuse. This is a^2 + b^2 = c^2. In our case, a is the width and b is the height. So, we must solve for c. To do this we plug in our values and solve. So, 3^2 + 5^2 = c^2. Then, 9 + 25 = c^2. Next, you add them up and square root both sides so you have sqrt(36) = c. The answer is 6 for c.
You have an apple tree in your backyard, and you pick 10 apples everyday. You're disappointed when you realize 2 apples everyday are rotten, so you throw them out. a.) Write an equation using 'x' as a variable to represent days. Also, the equation should be equal to 'y'. (Hint: 'y' is the total amount of apples kept after 'x' amount of days) b.) Solve for 'y', given you picked apples for 5 days
First, you read the problem sentence by sentence. The first sentence tells us that there are 10 apples being picked everyday. The second sentence tells us that we also throw out 2 apples everyday. a.) Now, we know we need to make an equation with the given information. If 'x' = days, then we can say 10*x-2*x. We can simplify this down to 8*x. Also, we must set this equation equal to y, for the total amount of apples. So, the finished equation will look like 8*x = y. b.) This part, we plug in a value for x to solve for y. Since you can't solve one equation with two unknowns without a system of equations. We are given x here in order to solve this equation for the total amount of apples picked within 5 days. Your answer should stem from 8*5 = y, then your solution is 40 = y. Therefore, 40 apples are picked in a 5 day period.
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