~Solve by the Substitution method
3x/2-y/3=-18
3x/4+2y/9=-9
0.1x+0.002y=0.04
5x+y=2
3x/2-y/3=-18
3x/4+2y/9=-9
0.1x+0.002y=0.04
5x+y=2
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1.) (3x / 2) - (y / 3) = - 18
6(3x / 2) - 6(y / 3) = 6(- 18)
9x - 2y = - 108
9x = 2y - 108
x = 2/9 y - 108/9
x = 2/9 y - 12 ........................... Eq. 1
(3x / 4) + (2y / 9) = - 9
36(3x / 4) + 36(2y / 9) = 36(- 9)
27x + 8y = - 324 ...................... Eq. 2
Sub 2/9 y - 12 from Eq. 1 for x in Eq. 2:
27(2/9 y - 12) + 8y = - 324
6y - 324 + 8y = - 324
14y = 324 - 324
14y = 0
y = 0
and
x = 2/9(0) - 12
x = - 12
Solution Set (- 12, 0)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
2.) 0.1x + 0.002y = 0.4
0.002y = - 0.1x + 0.4
1000(0.002y) = 1000(- 0.1x) + 1000(0.4)
2y = - 100x + 40
100x + 2y = 40
50x + y = 20 ................. Eq. 1
5x + y = 2
y = - 5x + 2 .................. Eq. 2
Sub - 5x + 2 from Eq. 2 for y in Eq. 1:
50x + (- 5x + 2) = 20
50x - 5x + 2 = 20
45x = 20 - 2
45x = 18
x = 18 / 45
x = 2/5
and
y = - 5(2/5) + 2
y = - 2 + 2
y = 0
Solution Set (2/5, 0)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
6(3x / 2) - 6(y / 3) = 6(- 18)
9x - 2y = - 108
9x = 2y - 108
x = 2/9 y - 108/9
x = 2/9 y - 12 ........................... Eq. 1
(3x / 4) + (2y / 9) = - 9
36(3x / 4) + 36(2y / 9) = 36(- 9)
27x + 8y = - 324 ...................... Eq. 2
Sub 2/9 y - 12 from Eq. 1 for x in Eq. 2:
27(2/9 y - 12) + 8y = - 324
6y - 324 + 8y = - 324
14y = 324 - 324
14y = 0
y = 0
and
x = 2/9(0) - 12
x = - 12
Solution Set (- 12, 0)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
2.) 0.1x + 0.002y = 0.4
0.002y = - 0.1x + 0.4
1000(0.002y) = 1000(- 0.1x) + 1000(0.4)
2y = - 100x + 40
100x + 2y = 40
50x + y = 20 ................. Eq. 1
5x + y = 2
y = - 5x + 2 .................. Eq. 2
Sub - 5x + 2 from Eq. 2 for y in Eq. 1:
50x + (- 5x + 2) = 20
50x - 5x + 2 = 20
45x = 20 - 2
45x = 18
x = 18 / 45
x = 2/5
and
y = - 5(2/5) + 2
y = - 2 + 2
y = 0
Solution Set (2/5, 0)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
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what college do you go to? I did this in 8th grade haha
substitution means you solve for one variable in terms of the other, then plug that value into the other equation to get a numerical answer.
so for the second one you can see that y=2-5x so you can plug 2-5x in for y in the first equation and solve for it.
i dont have paper so i cant really do the numbers
substitution means you solve for one variable in terms of the other, then plug that value into the other equation to get a numerical answer.
so for the second one you can see that y=2-5x so you can plug 2-5x in for y in the first equation and solve for it.
i dont have paper so i cant really do the numbers
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9x - 2y = -54
27x + 8y = -324
-2y = -9x - 54
y = 4.5x + 27
27x + 9(4.5x + 27) = -324
27x + 40.5x + 243 = -324
67.5x + 243 = -324
67.5x = 567
Divide, solve for x, and ten substitute for y.
y = -5x + 2
0.1x + 0.002(-5x + 2) = 0.04
0.1x - 0.01x + 0.004 = 0.04
0.11x + 0.004 = 0.04
0.11x = 0.036
27x + 8y = -324
-2y = -9x - 54
y = 4.5x + 27
27x + 9(4.5x + 27) = -324
27x + 40.5x + 243 = -324
67.5x + 243 = -324
67.5x = 567
Divide, solve for x, and ten substitute for y.
y = -5x + 2
0.1x + 0.002(-5x + 2) = 0.04
0.1x - 0.01x + 0.004 = 0.04
0.11x + 0.004 = 0.04
0.11x = 0.036
12
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