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Nitella [24]
3 years ago
10

write a system of linear equations that has only one solution. solve the system of equations in two ways.

Mathematics
1 answer:
Iteru [2.4K]3 years ago
7 0
X + 5y = 1 . . . . (1)
8x - 2y = 3 . . . .(2)
Solution 1.
From (1), x = 1 - 5y
substituting for x in (2), we have:
8(1 - 5y) - 2y = 3
8 - 40y - 2y = 3
8 - 42y = 3
42y = 5
y = 5/42
x = 1 - 5(5/42) = 1 - 25/42 = 17/42.

Solution 2.
Multiply (1) by 8, to get:
8x + 40y = 8 . . . . . (3)
(3) - (2) = 40y - (-2y) = 8 - 3
42y = 5
y = 5/42
substitute for y into (3), to get:
8x + 40(5/42) = 8
8x + 100/21 = 8
8x = 8 - 100/21 = 68/21
x = (68/21)/8 = 17/42
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What does the measure of B Equal?
defon
You have two triangles, ADC and ABC.
Sides AD and AB are congruent.
Sides DC and BC are congruent.
Side AC is congruent to itself.
By SSS, triangles ADC and ABC are congruent.

Corresponding parts of congruent triangles are congruent.
That means that angles DAC and BAC are congruent.
Angles DCA and BCA are congruent.

Since m<DAC = 32, then m<BAC = 32
Since m<DCA = 41, then m<BCA = 41.

Now you know the measures of two angles of triangle ABC.
The measures of the interior angles of a triangle add to 180.
You can find the measure of angle B.

m<BAC + m<B + m<BCA = 180

32 + m<B + 41 = 180

m<B + 73 = 180

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\boxed{\green{=  \frac{1}{15} x}}

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