Answer:
(3, 1)
Step-by-step explanation:
(a) Algebraic solution
(1) y = -⅔x + 3
(2) y = 2x - 5
Set Equation (1) equal to Equation (2)
-⅔x + 3 = 2x - 5
Multiply each side by 3
-2x + 9 = 6x - 15
Add 15 to each side
-2x + 24 = 6x
Add 2x to each side
24 = 8x
Divide each side by 3
(3) x = 3
Substitute (3) into (2)
y = 2×3 - 5 = 6 - 5 = 1
The ordered pair that makes both equations true is (3, 1).
(b) Graphical solution
In the diagram below, the red line is the graph of Equation (1). The blue line is the graph of Equation (2). The point of intersection is at (3, 1).
Answer:
(-1, -2)
Step-by-step explanation:
4x - 7y = 10
3x + 2y = -7
The common multiple of the x coefficient is 12.
Multiple 3 to 4 to get 12; 4 to 3 to 12:
3(4x - 7y = 10)
4(3x + 2y = -7)
12x - 21y = 30
12x + 8y = -28
Subtract the two equations:
-29y = 58
y = -2
Substitute y = -2 to either 4x - 7y = 10 or 3x + 2y = -7. Typically, do the easier equation to solve:
3x + 2(-2) = -7
3x - 4 = -7
3x = -3
x = -1
The order pair solution is like a coordinate: (x, y)
You are welcome!
Kayden Kohl
9th Grade Algebra II Student
Ratio of height of the flag pole to the length of its shadow = 40:9.6 = 25:6
Ratio of height of the building to the length of its shadow = x:48 = 25:6
x/48 = 25/6
x = (48 x 25)/6 = 1200/6 = 200
Therefore, the height of the building is 200 feet.
Answer: jason has 10 dimes and 5 quarters.
Step-by-step explanation:
The worth of a dime is 10 cents. Converting to dollars, it becomes
10/100 = $0.1
The worth of a quarter is 25 cents. Converting to dollars, it becomes
25/100 = $0.25
Let x represent the number of dimes that he has.
Let y represent the number of quarters that he has.
He has twice as many dimes as quarters. This means that
x = 2y
Jason has $2.25 worth of dimes and quarters. This means that
0.1x + 0.25y = 2.25 - - - - - - - - - - - 1
Substituting x = 2y into equation 1, it becomes
0.1 × 2y + 0.25y = 2.25
0.2y + 0.25y = 2.25
0.45y = 2.25
y = 2.25/0.45
y = 5
x = 2y = 2 × 5
x = 10
