Answer:
= 298/11
Step-by-step explanation:
3x + 5y = 2 | ×2 |
2x - 4y = 20 | ×3 |
6x + 10y = 4
6x - 12y = 60
____________--
22y = -56
y = -56/22
y = -28/11
3x + 5y = 2 | ×4 |
2x - 4y = 20 | ×5 |
12x + 20y = 8
10x - 20y = 100
_____________+
22x = 108
x = 108/22
x = 54/11
5x - y
= 5(54/11) - (-28/11)
= 270/11 + 28/11
= 298/11
Answer:
12x - 6
Step-by-step explanation:
multiply each expression in the parenthesis by 3
3(4x-2) = 12x - 6
You're trying to find constants
such that
. Equivalently, you're looking for the least-square solution to the following matrix equation.
To solve
, multiply both sides by the transpose of
, which introduces an invertible square matrix on the LHS.
Computing this, you'd find that
which means the first choice is correct.
Answer:
Solution: (3, 2)
Step-by-step explanation:
It's easier to graph when the equation of the lines are in their slope-intercept form, y = mx + b.
<u>x - 3y = -3</u>
-3y = -x - 3
Divide both sides by -3:
y = 1/3x + 1
where slope = 1/3
y-intercept = 1
<u>x + y = 5</u>
Subtract x from both sides to isolate y:
x - x + y = - x + 5
y = -x + 5
where slope = -1
y-intercept, 5
I started by graphing the y-intercepts of each line. Then, I used the slope of each linear equation (rise over run) to plot the next points on the graph. In the attached screenshot of the graph, <u>x - 3y = -3</u> is the blue line, while <u>x + y = 5</u> is the green line. Their intersection occurs at point, (3, 2).
Therefore, the solution is (3, 2).
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Answer:
C = 18.85
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr
R = radius
C = 2π(3)
C = 18.84955592