Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
2x - 3y = - 2 → (1)
4x + y = 24 → (2)
Multiplying (1) by - 2 and adding to (2) gives
- 4x + 6y = 4 → (3)
Add (2) and (3) term by term
(4x - 4x) + (y + 6y) = (24 + 4), that is
7y = 28 ( divide both sides by 7 )
y = 4
Substitute y = 4 into either of the 2 equations
Substituting y = 4 into (2)
4x + 4 = 24 ( subtract 4 from both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Thus the answers x = 5 and y = 4 are the same as her first method
First question
1:C 2:D 3:B 4:D
second question
0-2+5
The first option reduces to 1 and the second one reduces to -1.
As we go from (-6,6) to (9,1), x increases by 15 and y decreases by 5. Thus, the slope of this line is m = rise / run = -5/15, or m = -1/3.
Point-slope form: y-6 = (-1/3)(x+6), using data from (-6,6).
Slope-intercept form: starting with y = mx + b, substit. -6 for x, 6 for y and -1/3 for m:
6 = (-1/3)(-6) + b, or
6 = 2 + b. Then b = 4, and the equation in slope-intercept form is
y = (-1/3)x + 4.
Answer:
80 m^2
Step-by-step explanation:
The given information lets you write two equations involving length (x) and width (y).
- 2(x +y) = 36 . . . . the perimeter is 36 m
- (x+1)(y+2) -xy = 30 . . . . increasing the length and width increases area
The second of these equations simplifies to another linear equation, giving a system of linear equations easily solved.
xy +y +2x + 2 -xy = 30
2x +y = 28 . . . . . . . subtract 2
Dividing the first equation by 2 gives
x +y = 18
and subtracting this from the above equation gives ...
(2x +y) -(x +y) = 28 -18
x = 10
Then
y = 18 -10 = 8
The area of the original rectangle is xy = 10·8 = 80 m^2.
