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Answer:
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Step-by-step explanation:
Misha's group was asked to write an expression equivalent to
7y²z + 3yz² - 3
When Mr. Chen checked their answers, he found only one to be correct.
And she was Helena.
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Because, (7y²z + 6yz²- 5 - 3yz² + 2)
= 7y²z + (6yz² - 3yz²) - (5 - 2)
= 7y²z + 3yz² - 3 (Answer)
Answer:
Different ways to solve a system of linear equations:
- isolate one variable in one equation and replace it in the other equation
- multiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remains
- graph the equation and look at the intersection point
If you graph the system:
- there is only one solution if the lines intersects at only one point
- there is no solution if the lines don't intersect each other (they are parallel)
- there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)
Step-by-step explanation:
1st system
y = -x – 7
y = 4/3 x – 7
solution: x= 0, y = 7
2nd system
y = -3x – 5
y = x + 3
solution: x = -2, y = 1
3rd system
y = -2x + 5
y = 1/3 x – 2
solution: x = 3, y = -1
4th system
3x + 2y = 2
x + 2y = -2
solution: x = 2, y = -2
5th system
x + 3y = -9
2x – y = -4
solution: x = -3, y = -2
6th system
x – 2y = 2
-x + 4y = -8
solution: x = -4, y = -3
7th system
5x + y = -2
x + y = 2
solution: x = -1, y = -3
If you would like to write the equation in the above form, you can calculate this using the following steps:
x^2 - 8x + 13 = 0
(x - 4)^2 = x^2 - 8x + 16
(x - 4)^2 - 3 = 0
(x - 4<span>)^2 = 3
</span>
The correct result would be (x - 4<span>)^2 = 3.</span>