Solve the system of linear equations using any method you choose: -6x + 3y = 18 10x - y = 4
1 answer:
9514 1404 393
Answer:
(x, y) = (1.25, 8.5)
Step-by-step explanation:
I choose to put these equations into reduced general form, then use the "cross multiplication method" to solve.
2x -y +6 = 0
10x -y -4 = 0
d1 = 2(-1) -10(-1) = 8
d2 = -1(-4) -(-1)(6) = 10
d3 = 6(10) -(-4)(2) = 68
Solutions are ...
x = d2/d1 = 10/8 = 1.25
y = d3/d1 = 68/8 = 8.5
The solution is (x, y) = (1.25, 8.5).
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<em>Additional comment</em>
I like a graphing calculator for a quick and easy solution. When the values are not integers, I like an algebraic solution to see what the exact values are.
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The "cross multiplication method" is similar to Cramer's rule in that determinants of pairs of coefficients are computed. If you look up this method, videos will show you a variation that is slightly different. Here, we determined d1, d2, and d3 as the 2×2 determinant of the coefficients in adjacent columns of the array you get from the general form equations with the first column repeated:
In each pair, the determinant is the difference between the product of numbers on the down-diagonal and the product of numbers on the up-diagonal.
The determinants relate to the x- and y-values by ...
1/d1 = x/d2 = y/d3 ⇒ x = d2/d1, y = d3/d1
There is a Vedic solution method for linear equations that is similar to this, but starts from equations in standard form. As a consequence, the cross-differences are done in a different order.
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Standard form: ax +by = c
General form: ax +by +c = 0
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Step-by-step explanation:
Given:
Let,
point S( x₁ , y₁) ≡ ( -1 , 1)
point T( x₂ , y₂) ≡ (3 , -5)
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To Find:
Point M( x , y )= ?
Solution:
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Answer:
$20 per sweater.
Step-by-step explanation:
It is given that,
A store buys 7 sweaters for $42 and sells them for $182.
We need to find how much profit the store make per sweater.
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