6x + 4y = 24
2x - 4y = -8
We will use the addition method in solving this system of equation.
6x + 4y = 24
+ (2x - 4y = -8)
8x + 0 = 16
8x = 16
x = 16/8
x = 2
Let us substitute x by its value to get the value of y.
6x + 4y = 24
→ 6(2) + 4y = 24
12 + 4y = 24
4y = 24 - 12
4y = 12
y = 12/4
y = 3
2x - 4y = - 8
→ 2(2) - 4y = - 8
4 - 4y = - 8
-4y = - 8 - 4
-4y = -12
y = -12/-4
y = 3
So x = 2 and y = 3. → (2,3)
The true statement among the choices are:
A) The ordered pair that is the solution to the system lies in Quadrant I .
<span>B) The y-coordinate of the solution is 3.
</span><span>D) The x-coordinate of the solution is 2.</span>
Answer:
y = 2x + 1 ;
y - 3 = - 3(x - 1) ; y = - 3x + 6 ;
Independent ;
(1, 3)
Step-by-step explanation:
Given the data:
Sidewalk 1:
x __ y
2 _ 5
0 _ 1
Sidewalk 2:
x __ y
1 _ 3
3 _ -3
Equation for sidewalk 1 in slope - intercept form:
Slope intercept form:
y = mx + c
c = intercept ; m = slope
m = (change in y / change in x)
m = (1 - 5) / (0 - 2) = - 4 / - 2 = 2
Y intercept ; value of y when x = 0
(0, 1) ; y = 1
Hence, c = 1
y = 2x + 1
Sidewalk 2:
Point slope form:
y - y1 = m(x - x1)
m = slope
m = = (-3 - 3) / (3 - 1) = - 6/2 = - 3
Point (x1, y1) = (1, 3)
y - 3 = - 3(x - 1)
To slope intercept form:
y - 3 = - 3(x - 1)
y - 3 = - 3x + 3
y = - 3x + 3 + 3
y = - 3x + 6
Since the slope of both lines are different, intersection will be at single point and will have a single solution. This makes it independent.
Using substitution method :
y = 2x + 1 - - - (1)
y = - 3x + 6 - - - (2)
Substitute (1) into (2)
2x + 1 = - 3x + 6
2x + 3x = 6 - 1
5x = 5
x = 1
From (1)
y = 2(1) + 1
y = 2 + 1
y = 3
Coordinate of the point of intersection = (1, 3)
Answer:
If you draw this out, you can see that total fence equation will be:
2L + 4W = 1200
Simplify, divide by 2
L + 2W = 600
L = (600-2W)
:
Area;
A = L*W
Substitute (600-2W) for L:
A = (600-2W)*W
A = -2W^2 + 600W; a quadratic equation
:
The dimension that will produce the greatest area will be the "axis of symmetry
which is: x = %28-b%29%2F%282a%29
:
In this equation a=-2, b=600
W = %28-600%29%2F%282%2A-2%29
W = %28-600%29%2F%28-4%29
W = +150 ft is the width
:
Find the length
L = 600 - 2(150)
L = 300 ft is the length
:
We can say the a field 300 by 150 gives he greatest area
:
This illustrated on a graph where y axis is the area and x axis is the width:
Step-by-step explanation:
Mark because if you look at 0.(6) it is bigger than 0.(4)5
Answer:
63-9b
Step-by-step explanation:
9(7-b)
=9×7-9×b
=63-9b
