Graph and solve x+2y=4, x-2y=-8
1 answer:
Answer:
(x, y) = (-2, 3)
Step-by-step explanation:
In this form, it is easy to determine the x- and y-intercepts of each equation. That makes it easy to graph the first one, but not so easy to graph the second one on the given form.
The x-intercept is found by solving for x when y=0. In the two equations, the x-intercepts are ...
x = 4
x = -8 . . . . . . not shown on the given grid
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The y-intercepts are found by solving for y when x=0. In the two equations, the y-intercepts are ...
y = 4/2 = 2
y = -8/-2 = 4
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For the second equation, you can solve for y to put it in slope-intercept form.
x -2y = -8
x +8 = 2y . . . . . add 2y+8
y = 1/2x +4 . . . . . . . slope = 1/2, y-intercept = 4 (which we already knew)
This means the graph of the second equation will have a rise of 1 for each run of 2 units to the right. Working to the left from the y-intercept, we find another point to be (-2, 3), a point 2 left and 1 down from the y-intercept. This point is also on the line produced by the first equation, so (-2, 3) is the solution to the system.
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Female: Male:
60 35
96 109
26 31
n₁=no. of entries=3 n₂=no. of entries=3
s₁=sample standard s₂=sample standard
deviation=35.005 deviation=43.924
x₁=sample mean=60.666 x₂=sample mean=58.333
Here s and x are calculated from calculator.
Now,
for significance level
1-α=90%
1-α=0.9
α=0.1
α/2=0.05
As population variances are unknown for both Male and female so the best suitable formula is
(x₁ - x₂) ± tα/2,v₁ *
........1
where v(degree of fredom)=(s₁²/n₁+s₂²/n₂)² / ((s₁²/n₁)²/n₁-1)+(s₂²/n₂)²/n₂-1))
by putting values
v=3.81026
From Statistics table,
See the t table at α/2=0.05 and v=3.81026
use interpolation as v value is not in the table,
3.81026-3/4-3 = x-3.182/2.776-3.182
x= 2.853
by putting values in eq. 1 we get
(60.666-58.333) ± (2.853)*
2.333 ± 92.516 is the correct answer.
60 35
96 109
26 31
n₁=no. of entries=3 n₂=no. of entries=3
s₁=sample standard s₂=sample standard
deviation=35.005 deviation=43.924
x₁=sample mean=60.666 x₂=sample mean=58.333
Here s and x are calculated from calculator.
Now,
for significance level
1-α=90%
1-α=0.9
α=0.1
α/2=0.05
As population variances are unknown for both Male and female so the best suitable formula is
(x₁ - x₂) ± tα/2,v₁ *
........1
where v(degree of fredom)=(s₁²/n₁+s₂²/n₂)² / ((s₁²/n₁)²/n₁-1)+(s₂²/n₂)²/n₂-1))
by putting values
v=3.81026
From Statistics table,
See the t table at α/2=0.05 and v=3.81026
use interpolation as v value is not in the table,
3.81026-3/4-3 = x-3.182/2.776-3.182
x= 2.853
by putting values in eq. 1 we get
(60.666-58.333) ± (2.853)*
2.333 ± 92.516 is the correct answer.