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anonymous

  • one year ago

What is the solution to the system of equations? x+y = 6 x=y +5

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  1. anonymous
    • one year ago
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    x+y=6 and x+y=5 for the variables x and y. First, let's work on your first equation,x+y=6 This means, see if it can be simplified at all before attempting to solve it. x+y evaluates to x+y So, all-in-all, your first equation can be written as: x+y = 6 Now, let's work on your second equation,x+y=5 x+y evaluates to x+y So, all-in-all, your second equation can be written as: x+y = 5 After this initial survey of the equations, the system of equations we'll set out to solve is: x+y = 6 and x+y = 5 Let's start by solving x+y = 6 for the variable x. Move the y to the right hand side by subtracting y from both sides, like this: From the left hand side: y - y = 0 The answer is x From the right hand side: The answer is 6-y Now, the equation reads: x = 6-y To isolate the x, we have to divide both sides of the equation by the other variables around the x on the left side of the equation. and this is the final solution to your equation. Next, let's solve x+y = 5 for the variable y. Move the x to the right hand side by subtracting x from both sides, like this: From the left hand side: x - x = 0 The answer is y From the right hand side: The answer is 5-x Now, the equation reads: y = 5-x To isolate the y, we have to divide both sides of the equation by the other variables around the y on the left side of the equation. and this is the final solution to your equation. Now, plug the earlier result, x=6-y, in for x everywhere it occurs in y=5-x. This gives y=5-(6-y). Now all we have to do is solve this for y,to have our first solution. 6-y evaluates to 6-y 5 - 6 = -1 The answer is -1+y 5-(6-y) evaluates to -1+y Move the y to the left hand side by subtracting y from both sides, like this: From the left hand side: y - y = 0 The answer is 0 From the right hand side: y - y = 0 The answer is -1 Now, the equation reads: 0 = -1 To isolate the y, we have to divide both sides of the equation by the other variables around the y on the left side of the equation. The last step is to divide both sides of the equation by 0 like this: Sorry, can't divide by zero! Stop! Everything below this line is wrong. 0 ÷ 0 = 1 Sorry, can't divide by zero! Stop! Everything below this line is wrong. -1 ÷ 0 = 1 The solution to your equation is: 1 = 1 Lastly, to find the solution for x, we plug this answer for y into the earlier result that x=6-y. This gives x=6-(1). Now, simplify this. 6-(1) evaluates to 5 x= 5 So, the solutions to your equations are: x= 5 and y= 1

  2. anonymous
    • one year ago
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    x=5 and y=1

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