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Is (-1,5) the solution to {y=-1x+4 {y= -1/5x

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3 Answers

The solution to this system of equations can be determined by solving for the system.

You are given the following system of linear equations: 

     y = -x + 4   

     y = (-1/5)x

Since both equations are solved for y, you can set them equal to one another and solve for x first:

     -x + 4 = (-1/5)x

   add x to both sides of the equation

     -x + x + 4 = (-1/5)x + x

   multiply x by 5/5 so that the two like terms on the right hand side have a common denominator

      4 = (-1/5)x + (5/5)x

   combine the like terms on the right hand side by adding their coefficients 

      4 = (4/5)x

   solve for x by multiplying both sides of the equation by 5/4

      (5/4)•4 = (5/4)•(4/5)x

      5 = x

Solve for y by plugging in the solution to x into one of the equations from the system:

     y = (-1/5)x 

     y = (-1/5)•5

     y = -5/5

     y = -1

Therefore, the solution to the system is (5, -1). Since this is the only solution to the system, (-1, 5) is not a solution.

Since you are given a point, the easiest way to check if it's a solution is to just plug in the point. For both equations, when you plug in x= -1, you should get y=5. 

First equation: y= -1x+4 = -1*-1+4 = 1+4 =5. Since y=5, this point is on the first line.

Second equation: y= -1/5x = -1/5(-1) = 1/5. Since this is not 5, (-1,5) is not on the second line. 

If the point is not on both lines, it cannot be a solution to the equation.

y = -1x + 4

y = -1/5x

Is (-1, 5) a solution of the above system?

There are several ways to determine whether or not the solution set (-1, 5) is the solution for the system, I think one of the easiest methods to determine this is to simply substitute the possible solution into each equation and see if it checks out.

Remember (-1, 5( is an ordered pair, meaning the first value is always x and the second value is always y.

Begin substituting values for variables: always re-write equation that you are cheking

y = -1x + 4

5 = ? -1(-1) + 4

5 = 1 + 4

5 = 5 CHEKS OUT

NEXT SUBSTITUTE:

y = -1/5x

5 =-1/5(-1)

5 = 5 cheks

HENCE (-1, 5) is the solution set for the above system.