Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution? y = x + 5 y = –2x
– 1 A. (0, –1) B. (0, 5) C. (–2, 3) D. (–2, –1)
2 answers:
Look at the picture. Here I have inserted the two functions, the green is the first. Can you find the solution? I also included all the answers.
Answer:
C. (–2, 3)
Step-by-step explanation:
Given :
Solution :
Equation a : y=x+5
Equation b : y = -2x-1
We will use substitution method
Putting the value of y from equation a in equation b
⇒
⇒
⇒
⇒
⇒
Now substituting value of x in equation a to get value of y
⇒
⇒
⇒
Thus the solution of given system of equations is (-2,3)
Thus The Option C is correct.
We have also solved it by graphing the equations you can refer the attached figure.
You might be interested in
When you represent intervals on the number line, you're including full dots, excluding empty dots, and you're considering numbers highlighted by the line.
In the first case, you've highlighted everything before -2 (full dot, thus included), and everything after 1 (empty dot, excluded). So, the set would be
or, in interval notation,
In the second case, you are looking for all numbers between -3 and 5. This interval is symmetric with respect to 1: you're considering all numbers that are at most 4 units away from 1, both to the left and to the right.
This means that the difference between your numbers at 1 must be at most 4, which is modelled by
where the absolute values guarantees that you'll pick numbers to the left and to the right of 1.