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Let's start by calling the two numbers we are looking for x and y.
The sum of x and y is 30. In other words, x plus y equals 30 and can be written as equation A:
x + y = 30
The difference between x and y is 20. In other words, x minus y equals 20 and can be written as equation B:
x - y = 20
Now solve equation B for x to get the revised equation B:
x - y = 20
x = 20 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 30
20 + y + y = 30
20 + 2y = 30
2y = 10
y = 5
Now we know y is 5. Which means that we can substitute y for 5 in equation A and solve for x:
x + y = 30
x + 5 = 30
X = 25
Summary: The sum of two numbers is 30 and their difference is 20. What are the two numbers? Answer: 25 and 5 as proven here:
Sum: 25 + 5 = 30
Difference: 25 - 5 = 20
<h2>ꜰᴏʟʟᴏᴡ ᴍᴇ❤</h2>Answer:
Step-by-step explanation:
I'll assume these are the equations:
11x + y = 18
4x + y = 18
-2x - 2y = 18
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The easiest approach to graphing, for me, is to rearrange each to y=mx+b (slope-intercept) format:
- y = -11x+18 y-intercept of 18 (0,18)
- y = -4x + 18 y-intercept of 18 (0,18)
- y = - x -9 y-intercept of -9 (0,-9)
It seems to me that all three can be graphed easily from simply reading the slope and y-intercept values. Since these are straight lines, all we need is two points for each line, and one is standing out in plain view, the y-intercept: (0,y-intercept). The second point can be determined by using whatever value of x makes the calculation easy
An example: y = - x -9. Plot (0,-9) for the y intercept, and then calculate one additional point (e.g., for x = - 9). (-9,0) Then connect a straight line between these two points and presto (metric term for magic), a graph. For the first equation, I picked 20 for x. For x = 20, y = -29. That was easy, and we have the second point: (1,-10)
See the attachment for how this was done. The first points are all for the y-intercept (0,[18 or 9]). All of the second points were calculated in my head by using a convenient value for x.
This approach doesn't work well for non-linear equations. There, I find it easier to set up a table of values - a spreadsheet such as Excel is my tool for the calculations.
The attachment also demonstrates the Really Easy Way to graph functions. DESMOS, a free, and excellent, online calculator.
