a. we have two
lines: y = 4-x and
y = 8-x^-1
given two simultaneous equations that are both to be
true, then the solution is the points where the lines cross. the intersection is
where the two equations are equal. therefore the solution that works for both
equations is when
4-x = 8-x^-1
this is where the two lines will cross and that is the
common point that satisfies both equations.
b. 4-x = 8-x^-1
x 4-x 8-x^-1
-3 7
8.33
-2 6 8.5
-1 5 9
0 4
-
1 3
7
2 2
7.5
3 1 7.67
the table shows that none of the x values from -3 to 3 is
the solution because in no case does
4-x = 8-x^-1
to find the solution we need to rearrange the equation to
find for x:
4-x = 8-x^-1
multiply both sides with x:
4x-x^2 = 8x-1
x^2+4x-1=0
x= -4.236, 0.236
therefore there are two points that satisfies the
equation.
find y:
x=-4.236
y = 4-x = 4 β (-4.236)
= 8.236
y = 8-x^-1 = .236)^-1
= 8.236
x=0.236
y = 4-x = 4 β (0.236) = 3.764
y = 8-x^-1 = 8-(0.236)^-1
= 3.764
thus the two lines cross at 2 points:
(-4.236, 8.236) & (0.236, 3.764)
c. to solve
graphically the equation 4-x = 8-x^-1
we would graph both lines: y = 4-x and y
= 8-x^-1
the point on the graph where the lines cross is the
solution to the system of equations.
just graph the points on part b on a cartesian coordinate
system and extend the two lines. the
solution is, as stated, the point where the two lines cross on the graph.
step-by-step explanation:
mark brainliest!
