PLEASE HELP Find the area of the rectangle, to the nearest hundredth, with a base of 5 inches and a height = 2.5 inches. Type a
1 answer:
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Given:
The system of equations is:
Line A:
Line B:
To find:
The solution of given system of equations.
Solution:
We have,
...(i)
...(ii)
Equating (i) and (ii), we get
Divide both sides by 2.
Substituting in (i), we get
The solution of system of equations is (-4,-8).
Now verify the solution by substituting in the given equations.
This statement is true.
Similarly,
This statement is also true.
Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.
Answer:
Step-by-step explanation:
The equation of a line is y = mx + b
Where:
- m is the slope
- b is the y-intercept
First, let's find what m is, the slope of the line.
Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.
Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.
Now, just plug the numbers into the formula for m above, like this:
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
- (-3,1). When x of the line is -3, y of the line must be 1.
- (2,-1). When x of the line is 2, y of the line must be -1.
Now, look at our line's equation so far: .
is what we want, the -
is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want. The answer will be the same:
- (-3,1). y = mx + b or
, or solving for b:
.
.
- (2,-1). y = mx + b or
, or solving for b:
.
See! In both cases, we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-3,1) and (2,-1) is