Consider the following pair of equations: y = 3x + 3
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answers
The coordinate (x,y)=(-2,-3).
We have given the following pair of equations
y = 3x + 3.....(1)
y = x − 1.....(2)
Here we use the substitution method
What substitution method?
The value of one variable from one equation is substituted in the other equation
So the given system of linear equation
We have substitute the value of y from equation 2 into the value of y in equation one
So we get
x − 1= 3x + 3
add like terms
x-3x=3+1
-2x=4
x=4/-2
x=-2
Plug x=-2 in equation 2 we get,
y = -2 − 1
y=-3
Therefore we get the coordinate(x,y)=(-2,-3).
To learn more about the substitution method visit:
Take X=-2 into y
(x, y) =(-2,-3)
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Answers
In this question c squared is the diagonal you are trying to figure out.
A squared is any side of the triangle other than c squared, and b squared is the other side of the triangle. So a squared is 16 inches squared, and b squared is 12 inches squared.
To work this out, we square 16 to give 256.
Then 12 is squared - 144.
Then we square root 256 + 144, or the square root of 400.
The square root of 400 is 20, so the diagonal Luke cut was 20 inches long.
Final answer:
The length of the diagonal cut is calculated using the Pythagorean theorem. The sides of the paper form two sides of a right-angled triangle, and by squaring and adding these lengths, then taking the square root of the result, we find that the hypotenuse, or diagonal, is 20 inches long.
Explanation:
In mathematics, particularly in geometry, the Pythagorean theorem is the fundamental principle used to calculate the length of the hypotenuse in a right-angled triangle. In this question, the sheet of paper can be considered a rectangle and when it is cut from one corner to the opposite corner, it forms two right-angled triangles.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c²
Here, the length and width of the paper represent the two sides of the triangle, 16 inches and 12 inches respectively, and the diagonal cut (we'll call it 'd') is the hypotenuse. Thus, the equation becomes:
12² (which equals 144) + 16² (which equals 256) equals d²
Adding 144 and 256 gives 400, so d² = 400. To find 'd', we take the square root of 400, which is 20.
So, the length of the diagonal cut that Luke made is 20 inches.
Learn more about Pythagorean theorem here:
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