Our system of equations is:
y = x - 4
y = -x + 6
We can solve this system of equations by substitution. We already have one equation solved for the variable y in terms of x, so we can substitute in this equivalent value for y into the second equation as follows:
y = -x + 6
x - 4 = -x + 6
To simplify this equation, we first are going to add x to both sides of the equation.
2x - 4 = 6
Next, we are going to add 4 to both sides of the equation to separate the variable and constant terms.
2x = 10
Finally, we must divide both sides by 2, to get the variable x completely alone.
x = 5
To solve for the variable y, we can plug in our solved value for x into one of the original equations and simplify.
y = x - 4
y = 5 - 4
y = 1
Therefore, your final answer is x = 5 and y = 1, or as an ordered pair (5,1).
Hope this helps!
