Determine whether the point (1, 8) is a solution of the system
2x + 6y = 50
10x + 0y = 10
by substituting the point into each equation.
So far I have:
2x=6y=50
y=50-2x
10x+10y=10
10x+0(50-2x)=10
10x+0=10
x=10
y=50-2x
y=50-2(1)
y=50-2
y=48
PLEASE HELP! I'm lost. I've had tutoring and still do not understand fully.
To determine whether the point (1, 8) is a solution to the system of equations, you need to substitute the given values of x and y into each equation and check if both equations are true.
Let's start by substituting the point (1, 8) into the first equation:
2x + 6y = 50
Replacing x with 1 and y with 8:
2(1) + 6(8) = 50
2 + 48 = 50
50 = 50
The equation evaluates to true when substituting the values of (1, 8) into the first equation.
Now let's substitute the point (1, 8) into the second equation:
10x + 0y = 10
Replacing x with 1 and y with 8:
10(1) + 0(8) = 10
10 + 0 = 10
10 = 10
The equation also evaluates to true when substituting the values of (1, 8) into the second equation.
Since both equations are true when substituting (1, 8), the point (1, 8) is indeed a solution to the system of equations.
To determine whether the point (1, 8) is a solution of the system, we need to substitute the values of x and y into each equation and check if the equations are true.
Equation 1: 2x + 6y = 50
Substituting x = 1 and y = 8,
2(1) + 6(8) = 2 + 48 = 50
Since the equation is true, the point (1, 8) satisfies equation 1.
Equation 2: 10x + 0y = 10
Substituting x = 1,
10(1) + 0(8) = 10 + 0 = 10
Again, the equation is true, so the point (1, 8) also satisfies equation 2.
Since the point (1, 8) satisfies both equations in the system, it is a solution to the system.
Please note that your initial calculations seem to have errors. Let me take you through the correct steps again:
Equation 1: 2x + 6y = 50
Substituting x = 1 and y = 8:
2(1) + 6(8) = 2 + 48 = 50 (which verifies the equation)
Equation 2: 10x + 0y = 10
Substituting x = 1 and y = 8 (the value of y doesn't affect the equation since it's multiplied by 0):
10(1) + 0(8) = 10 + 0 = 10 (which verifies the equation)
Therefore, the point (1, 8) is indeed a solution of the system.
Plug x=1 and y=8 into the two equations simultaneously and see if both are satisfied.
They both are.
2 + 48 = 50
10 = 10
Therefore (1,8) is the solution.
Your equation y=50-2x
is wrong.
You are confusing SOLVING the two equations (which is possible by various means) with TRYING OUT a sample solution you have been given, to see if it works.
You have made the problem harder than it really is, and made mistakes in the process.