Which of the following would be a possible solution to the system of inequalities given below?
1 answer:
Answer:
(0,5)
Step-by-step explanation:
we have
----> inequality A
----> inequality B
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities of the system (makes true both inequalities)
Verify each ordered pair
Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B and then compare the results
case 1) (0,5)
For x=0,y=5
<em>Inequality A</em>
----> is true
so
The ordered pair satisfy inequality A
<em>Inequality B</em>
---> is true
so
The ordered pair satisfy inequality B
therefore
The ordered pair would be a solution of the system
case 2) (5,2)
For x=5,y=2
<em>Inequality A</em>
----> is true
so
The ordered pair satisfy inequality A
<em>Inequality B</em>
---> is not true
so
The ordered pair not satisfy inequality B
therefore
The ordered pair is not a solution of the system
case 3) (0,4)
For x=0,y=4
<em>Inequality A</em>
----> is not true
so
The ordered pair not satisfy inequality A
therefore
The ordered pair is not a solution of the system
case 4) (6,0)
For x=6,y=0
<em>Inequality A</em>
----> is not true
so
The ordered pair not satisfy inequality A
therefore
The ordered pair is not a solution of the system
You might be interested in
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