3.1 Homework: simultaneous equations by graphing

$\mathrm{2y}=\mathrm{6x}+\text{10}$ and $\mathrm{3y}=\text{12}x+9$

• a Put both equations into $y=\text{mx}+b$ format. Then graph them.
• b List all points of intersection.
• c Check these points to make sure they satisfy both equations.

$y=\mathrm{2x}-3$ and $\mathrm{3y}=\mathrm{6x}+3$

• a Put both equations into $y=\text{mx}+b$ format. Then graph them.
• b List all points of intersection.
• c Check these points to make sure they satisfy both equations.

$y=x-3$ and $\mathrm{2y}=\mathrm{2x}-6$

• a Put both equations into $y=\text{mx}+b$ format. Then graph them.
• b List all points of intersection.
• c Check these points to make sure they satisfy both equations.

$y=x$ and $y=x^2-1$

• a Graph them both on the back.
• b List all points of intersection.
• c Check these points to make sure they satisfy both equations.

$y=x^2+2$ and $y=x$

• a Graph them both on the back.
• b List all points of intersection.
• c Check these points to make sure they satisfy both equations.

$y=x^2+4$ and $y=\mathrm{2x}+3$

• a Put the second equation into $y=\text{mx}+b$ 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? ___________

$y=\frac{\mathrm{6x}}{x^2+1}$ and $y=4\sqrt{x}-5$

• 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.