Question

Graph each equation. Determine the solution of the system of equations. Use pencil and paper. Explain how to find the equation of a line that intersects the system of equations at the same point.

1) x=y
2) 4x= 3y - 3

Answer 1

9514 1404 393

Answer:

see attached

use the point-slope form

Explanation:

Substitution works to find the solution.

4x = 3x -3

x = -3 = y

The solution is (x, y) = (-3, -3).

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The first equation graphs as a line through the origin with a slope of 1.

The second equation graphs as a line through (0, 1) with a slope of 4/3, that is, a rise of 4 for each run of 3.

The two lines intersect at (x, y) = (-3, -3), so that point, together with the y-intercepts, can be used to draw the lines.

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A line that intersects point (-3, -3) can be written in point-slope form as ...

y +3 = m(x +3) . . . . . for some slope m.

If you were to choose m = -1, this becomes ...

y +3 = -(x +3)

y = -x -6 . . . . . . rearranged to slope-intercept form