Question

PLEASE HELP SOVLE THESE:

Solve the simultaneous equations: 2x + 3y = 10 x - y = 5
Solve 2x + 16 ≥ -8
Find the gradient and the coordinates of the y-intercept for the graph:
y - 12 = 3x
Find the gradient of the line that passes through the points
(1, 3) and (5, 11)
Find the coordinates of the midpoint of the line segment AB, where A and B have coordinates: A(-3, 0), B(9, -2)
A fair, six-sided dice is rolled 120 times. How many times would you expect to roll a 5?
Write down an equation of a straight line parallel to the line y = -2x + 3

Answer 1

2x + 3y = 10
x - y = 5....x = y + 5

2(y + 5) + 3y = 10
2y + 10 + 3y = 10
5y = 10 - 10
5y = 0
y = 0

x - y = 5
x - 0 = 5
x = 5

solution is (5,0)
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y - 12 = 3x.....y = 3x + 12...in y = mx + b form the gradient (slope) is in the m position and the y int is in the b position

y = 3x + 12......slope(gradient) = 3 and y int = 12 or (0,12)
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(1,3)(5,11)
slope(gradient) = (y2 - y1) / (x2 - x1)
(1,3)....x1 = 1 and y1 = 3
(5,11)....x2 = 5 and y2 = 11
now we sub
slope = (11 - 3) / (5 - 1) = 8/4 = 2 <== ur gradient
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midpoint formula : (x1 + x2) / 2 : (y1 + y2) / 2
(-3,0)....x1 = -3 and y1 = 0
(9,-2)...x2 = 9 and y2 = -2
now we sub
m = (-3 + 9) / 2 : (0 + (-2) / 2
m = 6/2 : -2/2
m = (3,-1) <===
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y = -2x + 3....slope here is -2. A parallel line will have the same slope.
So one parallel line is : y = -2x + 4......that last number can be any number except 3. So another parallel line could be : y = -2x + 2