Download Graph each of the following systems 22. 3x – 5y=-9 5x -6y=

Graph each of the following systems 22. 3x – 5y=-9 5x -6y= -8
23. 4x + 5y= -2 4y – x = 11
Solve each system by substitution. Determine whether the equations are
independent, dependent, or inconsistent. 36. y= -3x + 19 Y= 2x – 1
Plug the first into the second:
-3x+19 = 2x-1
Add 3x:
19 = 5x-1
Add 1:
20 = 5x
X=4
Get y:
Y = -3*4 + 19 = -12 + 19 = 7
So:
X = 4, y = 7 (independent, consistent)
38. y= -4x – 7 Y= 3x
Plug the second equation into the first:
3x = -4x – 7
Add 4x:
7x = -7
X = -1
Get y:
Y = 3x = 3*-1 = -3
So:
X = -1, y = -3 (independent, consistent)
Solve each system by substitution. Determine whether the equations are
independent, dependent, or inconsistent. 42. y= x + 4 3y – 5x= 6
Plug the first into the second:
3(x+4)-5x=6
3x+12 – 5x = 6
-2x + 12 = 6
Subtract 12:
-2x = -6
X=3
Get y:
Y = x+4 = 3+4 = 7
So:
X = 3, y = 7, independent, consistent
56. 2x – y= 4 2x – y= 3
Substitute the 2x-y from the first into the second:
4=3
That’s not true, so there are no solutions. inconsistent.
70. x + 3y= 2 -x + y= 1
Subtract 3y from the first:
X = 2-3y
Plug that into the second:
-(2-3y)+y = 1
-2+3y+y = 1
-2+4y = 1
4y = 3
Y = 3/4
Get x:
X = 2-3y
X = 2-3*3/4 = 2-9/4 = -1/4
So:
X = -1/2, y = ¾, independent, consistent
Exercises 7.2 Solve each system by addition. 8. x + y= 7 X – y = 9
Add the equations:
2x=16
X=8
Get y:
x+y=7
8+y=7
Y = -1
So:
X = 8, y = -1, consistent, independent
12. x – 2y= -1 -x + 5y= 4
Add them:
3y = 3
Y=1
Get x:
x-2*1 = -1
x-2 = -1
x=1
So:
X = 1, y = 1, independent, consistent
16. 3x + 5y= -11 X – 2y= 11
Multiply the second by -3:
-3x+6y=-33
Add that to the first:
11y = -44
Y = -4
Get x:
3x + 5*-4 = -11
3x – 20 = -11
3x = 9
X=3
So:
X = 3, y = -4, independent, consistent
22. 2x= 2- y 3x + y= -1
Add them:
2x-1 = 3x+2
-1 = x + 2
X = -3
Get y:
3x + y = -1
3*-3 + y = -1
-9 + y = -1
Y=8
So:
X = -3, y = 8, consistent, independent
Solve each system by the addition method. Determine whether the equations are
independent, dependent, or inconsistent. 26. x – y= 3 -6x + 6y = 17
Multiply the first by 6:
6x-6y = -18
Add to the other one:
0 = -1
That’s not true, so no solution, inconsistent.
36. 3/7x + 5/9y= 27 1/9x + 2/7y = 7
Multiply both equations by 63 to clear the fractions:
27x + 35y = 1701
7x + 18y = 441
Now, multiply the first by 7 and the second by -27:
189x + 245y = 11907
-189x - 486y = -11907
Add them:
-241y = 0
So y = 0.
Get x:
189x = 11907
Divide by 189:
x = 63
so:
x = 63, y = 0
Independent, consistent
44. 3x – 2.5y= 7.125 2.5x – 3y= 7.3125
Multiply by 16.
48x – 40y = 114
40x – 48y = 117
Multiply the first by 10 and the second by -12:
480x – 400y = 1140
-480x + 576y = -1404
Add:
176y = -264
Y = 1.5
Get x:
3x – 2.5*1.5 = 7.125
X = 1.125
So:
x = 1.125, y = -1.5
consistent, independent