PLEASE HELP, please write it out in the system of equations (step by step)
2 answers:
Answer:
Step-by-step explanation:
[1] 2x + y = -1
[2] x - 2y = -8 <------- given linear equations
Graphic Representation of the Equations : ----> given in attatchment
y + 2x = -1 -2y + x = -8 < ----- point where they connect is shown in graph
Solve by Substitution :
// Solve equation [2] for the variable x
[2] x = 2y - 8
// Plug this in for variable x in equation [1]
[1] 2•(2y-8) + y = -1
[1] 5y = 15
// Solve equation [1] for the variable y
[1] 5y = 15
[1] y = 3
// By now we know this much :
x = 2y-8
y = 3
// Use the y value to solve for x
x = 2(3)-8 = -2
Solution :
{x,y} = {-2,3}
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Distribute the sum:
Use the following formulas:
In case you don't know where those formulas came from:
The first one is obvious; you're just adding <em>n</em> copies of 1, so 1 + 1 + ... + 1 = <em>n</em>.
The second can be proved in this way: let <em>S</em> be the sum 1 + 2 + 3 + ... + <em>n</em>. Rearrange it as <em>S</em> = <em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2) + ... + 1. Then 2<em>S</em> = (<em>n</em> + 1) + (<em>n</em> + 1) + (<em>n</em> + 1) + ... + (<em>n</em> + 1), or <em>n</em> copies of <em>n</em> + 1. So 2<em>S</em> = <em>n</em>(<em>n</em> + 1). Divide both sides by 2 and we're done.