I am having a really hard time with these!
1. Solve system of equations
x+3y=7 (1)
x=8-3y (2)
2. find slope
(9,8) (10,-7)
3. translate into an algebraic expression
The product of 46% and some number
1. Substitute 8-3y for y in the first equation and solve the reulting equation in y only.
2. The slope of the line connecting those points is the change in y divided by the change in x between the two points.
3. If "some number" is called x, 46% of that number is 0.46 x
Please make an effort to solve these yourself and show your work if you need further help
1. Solve system of equations
x+3y=7 (1)
x=8-3y (2)
You can "substitute", use the x from the first equation in the second like this:
x = 7 - 3 y from first, use in second
7 -3y = 8 -3y
As you can see, that is impossible. You have been given a set of equations that represent two parallel lines that never cross. There is no solution.
2. find slope
(9,8) (10,-7)
chnge in y / change in x
= (-7 - 8) / (10 - 9)
= -15/1
= -15
3. translate into an algebraic expression
The product of 46% and some number
46%/100 = 0.46
so
y = 0.46 x
I'd be happy to help you with these problems! Let's tackle each one step by step:
1. Solve system of equations:
To solve this system of equations, you can use the method of substitution or elimination. Let's use substitution in this case:
First, let's solve equation (2) for x:
x = 8 - 3y
Now, substitute this value of x into equation (1):
(8 - 3y) + 3y = 7
Simplifying the equation, we get:
8 - 3y + 3y = 7
8 = 7
Uh-oh! This equation is not true. This means that these two equations are inconsistent and have no solution.
2. Find slope:
To find the slope of a line given two points, we use the formula: slope = (change in y) / (change in x)
Let's use the coordinates (9,8) and (10, -7) to find the slope:
change in y = -7 - 8 = -15
change in x = 10 - 9 = 1
Now, we can calculate the slope:
slope = (-15) / 1 = -15
So, the slope is -15.
3. Translate into an algebraic expression:
The statement "The product of 46% and some number" can be translated into an algebraic expression using the following steps:
- "46%" can be written as the decimal 0.46.
- "Some number" can be represented by the variable 'x'.
Multiplying them together, we get:
0.46 * x
So, the algebraic expression for "The product of 46% and some number" is 0.46x.
I hope this helps! If you have any further questions, feel free to ask.