Graphing Solutions of Systems
- Thread starter Lyphta
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- Feb 4, 2004
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If you must solve "by graphing" (a poor way of solving, when algebra is available), then you can either graph the equations as they stand:
. . . . .x = y<sup>2</sup> - 5y + 4
. . . . .x + y = 1
...or you could at least rearrange the second equation a bit:
. . . . .x = y<sup>2</sup> - 5y + 4
. . . . .y = -x + 1
To graph the first equation, you'd do your T-chart, same as always, but you'd put the y-column first, instead of the x-column. Then pick y-values, plug them in to find the x-values, and fill in the chart. Just remember that the values are backwards when it comes to drawing your dots. Naturally, you'll get a sideways parabola.
On the other hand, if you'd prefer to be picking x-values, or if you'd like to plug into your graphing calculator, rearrange the first equation as:
. . . . .y<sup>2</sup> - 5y + (4 - x) = 0
Then apply the Quadratic Formula to solve for "y=" in terms of x, using a = 1, b = -5, and c = 4 - x. Because of the square root part, you'll get two pieces. When you graph them, they'll join to form that sideways parabola.
Otherwise, the graphing is the same as all the other quadratics you've graphed. Just remember to do this very neatly, since you'll be trying to read an exact answer from the picture you draw.
Eliz.
. . . . .x = y<sup>2</sup> - 5y + 4
. . . . .x + y = 1
...or you could at least rearrange the second equation a bit:
. . . . .x = y<sup>2</sup> - 5y + 4
. . . . .y = -x + 1
To graph the first equation, you'd do your T-chart, same as always, but you'd put the y-column first, instead of the x-column. Then pick y-values, plug them in to find the x-values, and fill in the chart. Just remember that the values are backwards when it comes to drawing your dots. Naturally, you'll get a sideways parabola.
On the other hand, if you'd prefer to be picking x-values, or if you'd like to plug into your graphing calculator, rearrange the first equation as:
. . . . .y<sup>2</sup> - 5y + (4 - x) = 0
Then apply the Quadratic Formula to solve for "y=" in terms of x, using a = 1, b = -5, and c = 4 - x. Because of the square root part, you'll get two pieces. When you graph them, they'll join to form that sideways parabola.
Otherwise, the graphing is the same as all the other quadratics you've graphed. Just remember to do this very neatly, since you'll be trying to read an exact answer from the picture you draw.
Eliz.
