In each problem, find all
x
x
size 12{x} {}
and
y
y
size 12{y} {}
values that satisfy both conditions. Your answers may be approximate.
2y=6x+102y=6x+10 size 12{2y=6x+"10"} {} and
3y=12x+93y=12x+9 size 12{3y="12"x+9} {}
- a. Put both equations into
y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them.
- b. List all points of intersection.
- c. Check these points to make sure they satisfy both equations.
y
=
2x
−
3
y
=
2x
−
3
size 12{y=2x - 3} {}
and
3y
=
6x
+
3
3y
=
6x
+
3
size 12{3y=6x+3} {}
- a. Put both equations into
y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them.
- b. List all points of intersection.
- c. Check these points to make sure they satisfy both equations.
y=x−3y=x−3 size 12{y=x - 3} {} and
2y=2x−62y=2x−6 size 12{2y=2x - 6} {}
- a. Put both equations into
y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them.
- b. List all points of intersection.
- c. Check these points to make sure they satisfy both equations.
y
=
x
y
=
x
size 12{y=x} {}
and
y
=
x
2
−
1
y
=
x
2
−
1
size 12{y=x rSup { size 8{2} } - 1} {}
- a. Graph them both on the back.
- b. List all points of intersection.
- c. Check these points to make sure they satisfy both equations.
y
=
x
2
+
2
y
=
x
2
+
2
size 12{y=x rSup { size 8{2} } +2} {}
and
y
=
x
y
=
x
size 12{y=x} {}
- a. Graph them both on the back.
- b. List all points of intersection.
- c. Check these points to make sure they satisfy both equations.
y
=
x
2
+
4
y
=
x
2
+
4
size 12{y=x rSup { size 8{2} } +4} {}
and
y
=
2x
+
3
y
=
2x
+
3
size 12{y=2x+3} {}
- a. Put the second equation into
y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them both on the back.
- b. List all points of intersection.
- c. Check these points to make sure they satisfy both equations.
Time for some generalizations…
- a. When graphing two lines, is it possible for them to never meet? _______
- To meet exactly once? _________
- To meet exactly twice? _________
- To meet more than twice? ___________
- b. When graphing a line and a parabola, is it possible for them to never meet? _______
- To meet exactly once? _________
- To meet exactly twice? _________
- To meet more than twice? ___________
This last problem does not involve two lines, or a line and a parabola: it’s a bit weirder than that. It is the only problem on this sheet that should require a calculator.
y
=
6x
x
2
+
1
y
=
6x
x
2
+
1
size 12{y= { {6x} over {x rSup { size 8{2} } +1} } } {}
and
y
=
4
x
−
5
y
=
4
x
−
5
size 12{y=4 sqrt {x} - 5} {}
- a. Graph them both on your calculator and find the point of intersection as accurately as you can.
- b. Check this point to make sure it satisfies both equations.
"This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"