I could really use some help. Is it
yes
no
not enough info
no solution
I could really use some help. Is it
yes
no
not enough info
no solution
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.