Solve the given system using your choice of either graphically or algebraically. Show and explain all work. y = 3x + 2 y = -2x + 7like i dont get what to do like whats the steps and how did you get those numbers for the steps
Answers
Answer:
Solution: x = 1, y = 5 or (1, 5).
Step-by-step explanation:
Given the systems of linear equations, y = 3x + 2 and y = -2x + 7:
I will demonstrate both solving for the solutions algebraically and graphically.
Algebraic Method:
Equation 1:y = 3x + 2
Equation 2: y = -2x + 7
Substitute the value of y = 3x + 2 from Equation 1 into Equation 2:
Equation 2: y = -2x + 7
⇒ 3x + 2 = -2x + 7
Add 2x to both sides:
3x + 2x + 2 = -2x + 2x + 7
5x + 2 = 7
Subtract 2 from both sides:
5x + 2 - 2 = 7 - 2
5x = 5
Divide both sides by 5 to isolate x:
x = 1
Substitute the value of x into Equation 1 to solve for y:
Equation 1: y = 3x + 2
y = 3(1) + 2
y = 3 + 2
y = 5
Therefore, the solution to the given system is x = 1, y = 5 or (1, 5).
Verify:
Substitute the value of x = 1, and y = 5 into both equations:
Equation 1:y = 3x + 2
y = 3x + 2
5 = 3(1) + 2
5 = 5 (True statement)
Equation 2: y = -2x + 7
y = -2x + 7
5 = -2(1) + 7
5 = -2 + 7
5 = 5 (True statement).
Hence, we have the correct solution to both equations.
Graphing Method:
In order to solve for the solution graphically, start by plotting the y-intercepts of both equations.
Equation 1:y = 3x + 2
Slope = 3, y-intercept: (0, 2)
Equation 2: y = -2x + 7
Slope = -2, y-intercept: (0, 7)
After plotting the y-intercepts, use the slope (rise over run technique) of each equation to plot other points into the graph. In other words:
In Equation 1, the slope = 3 (rise 3 units, run 1 unit to the right).
For Equation 2, the slope = -2 (down 2 units, run 1 unit to the right).
Continue this process until you have at least 3 points to connect your line with.
The solution will be the point where the two lines intersect, which occurs at point (1, 5).
Attached is a screenshot of the graphed equations.
Answer:
(1, 5) I think this supposed to be the answer you are looking for! I rlly hope this helps!
Step-by-step explanation:
y = 3x + 2 y = -2x + 7
= take the first equation and use the 3x + 2 and replace the y in the second equation with that!
3x + 2 = -2x + 7
= 3x + 2x = 7 - 2
= 5x = 5
= x = 1
Now substitute x for one!
y= 3 x 1 + 2
y= 5
Now try the other equation, to be sure!( If you wanna, I mean, you should...)
y= -2 x 1 + 7
y= -2 + 7
y= 5
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B) 19
C) 21
D) 23
Answers
The solution is Option D.
The value of the inequality equation is x < 22
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
x - 8 < 14 be equation (1)
Now , the value of equation can be simplified as
x - 8 < 14
Adding 8 on both sides of the equation , we get
x < ( 14 + 8 )
The value of x < 22
Therefore , the value of x is always less than 22
Hence , the value of the inequality equation is x < 2
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Answer:
D 23
Step-by-step explanation:
Answers
21 divided by 4
It can either be solved by using a calculator or long division
And we will end up with the answer:5.25
24 is 16% of what number
Answers
It is found that 24 is 16% of number 3.84.
To determine what number 24 is 16% of, we can use the formula:
Consider a proportion as;
(number) = (16%)*(24) / 100
To Convert 16% to decimal form by dividing it by 100:
16/100 = 0.16
Then Multiply the decimal form of 16% by 24:
0.16 * 24 = 3.84
Therefore, 24 is 16% of 3.84.
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B) Fall 3°F
C) Rise 8°F
D) Rise 5°F
Answers
71 - 5 = 66 degrees
then it rises 8 degrees
66 + 8 = 74 degrees
How much does the temp have to rise or fall to get back to 71...
74 - 71 = 3 degrees
It has to fall 3 degrees F. Answer B.
B. Fall 3°F is your answer.
Answers
B.1/7 of a pitcher
C.3/8 of a pitcher
D.8/3 of a pitcher