algebra a system with no solution pg.453 and more

pg. 453 ex. 453

ex. 3

2x-3y=6
3y-2x=3

solution:

first write the equation in y slope intercept form;

2x-3y=6
-3y=-2x+6
y=2/3x-2
the +6 is taken off and the 2 is divided by 3x then bring the -2 with the equation.

3y-2x=3
3y=2x+3
the 3y is kept, the -2x on the left side becomes 0, bring the 2x on to the right side of the= sign then the - becomes a +.
y=2/3x+1

since the slope is the same 2/3, the lines then are paralell, with a 0 with a line through it to indicate the solution set as empty.

17. pg, 459

2y-2x=2
2y-2x=6

first rewrite the equation in slope intercept form;
y=x+1 and y=x+3
the lines are paralell with no solution and an empty set.

ex. 3 ch. 3 pg. 215

using point slope form with parallel lines:

find the equation of each line. Write the answer in slope intercept form.
a) the line through (2,-1) that is parallel to y=-3x+9

solution: the slope of y=-3x+9 and any line parallel to it is -3.
now use the point (2,-1) and slope -3 in point slope form.

y-y1=m(x-x1) point slope form.
y-(-1)=-3(X-2) substitution
y+1=3x+6 simplify
y=-3x+5 slope intercept form
since -1 = -3(2)+5 is correct, the line y=-3x+5 goes through (2,-1). It is parellel to y=-3x+9. So y=-3x+5 is the desired equation.

that is all for now.
Marie Zajac BA in Psychology with a Concentration in Rehabilitaion in Counseling.