find the solution to the system of equations by using either graphing and substitution y = 6 - x and y = x - 2
(2,4)
(-4,2)
(4,2)
no solutions
I think this one is the third answer am I right?
correct
Very much need help
What the answer to the whole assignment
To find the solution to the system of equations, you can use either graphing or substitution.
To solve by graphing, plot the two equations on a coordinate plane. The first equation is y = 6 - x, and the second equation is y = x - 2. By graphing these two lines, you can determine where they intersect, which represents the solution to the system.
To solve by substitution, you can substitute one equation into the other and then solve for one variable. Let's use the second equation, y = x - 2, and substitute it into the first equation. So, we have y = 6 - x = x - 2. By rearranging the equation to isolate one variable, we get 2x = 8, which leads to x = 4. Now, substitute this value of x back into either equation to solve for y. If we use the second equation, y = x - 2, we get y = 4 - 2, which is y = 2. So, the solution to this system of equations is (4, 2).
Now, let's check whether any of the given points (2,4), (-4,2), and (4,2) satisfy both equations. Plugging in the values of x and y from each point into the two equations, we can determine if they hold true.
For (2,4):
y = 6 - x --> 4 = 6 - 2, which is true
y = x - 2 --> 4 = 2 - 2, which is not true
For (-4,2):
y = 6 - x --> 2 = 6 - (-4), which is true
y = x - 2 --> 2 = -4 - 2, which is not true
For (4,2):
y = 6 - x --> 2 = 6 - 4, which is true
y = x - 2 --> 2 = 4 - 2, which is true
Therefore, out of the given points, only (4,2) satisfies both equations. Thus, the correct answer is that the solution to the system of equations is (4,2).