The solution to the system of equations 5x-3y=6 and 2x-5y=10 is x = 0 and y = -2.
To find the solution to the system of equations:
5x - 3y = 6 ...(1)
2x - 5y = 10....(2)
Use the elimination method to find the solution:
Multiply both sides of equation (1) by 2 to make the coefficients of 'x' in both equations equal:
2(5x - 3y) = 2(6)
10x - 6y = 12
Now, we have the following two equations:
10x - 6y = 12
2x - 5y = 10
Multiply both sides of equation (2) by 5 to make the coefficients of 'y' in both equations equal:
5(2x - 5y) = 5(10)
10x - 25y = 50
Now, we have the following two equations:
10x - 6y = 12...(3)
10x - 25y = 50...(4)
Subtract equation (3) from equation (4) to eliminate 'x':
(10x - 25y) - (10x - 6y) = 50 - 12
-19y = 38
Divide both sides by -19 to solve for 'y':
y = 38 / -19
y = -2
Now that we have the value of 'y', substitute it back into either equation (1) or (2) to find 'x'.
Use equation (1):
10x - 6(-2) = 12
10x + 12 = 12
Subtract 12 from both sides:
10x = 0
x = 0
So, the solution to the system of equations is x = 0 and y = -2.
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If x represents the number of pieces of fruit Janet ate, then Sylvia ate 2 * (x+4) pieces of fruit based on the given question.
The question requires an algebraic expression to show how many pieces of fruit Sylvia ate. According to the question, Tom ate four more pieces of fruit than Janet. If x is the number of fruits Janet ate, then we can represent the number of fruits Tom ate as x + 4.
Next, the question states that Sylvia ate twice as many pieces of fruit as Tom. So, we can represent the number of pieces of fruit Sylvia ate as 2 * (x+4). Hence, this is the expression that represents the amount of fruit that Sylvia ate.
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Answer:
k = 3
Step-by-step explanation:
If the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9, then their slopes are equal
For coordinate AB;
slope m1 = 3 - 3k/k-(-1)
m1 = 3-3k/k+1
For the line 2y+3x = 9
2y = -3x + 9
y = -3/2 x + 9/2
Slope m2 = -3/2
Since m1 = m2
3-3k/k+1 = -3/2
Cross multiply
2(3-3k) = -3(k+1)
Expand
6 - 6k = -3k - 3
-6k+3k = -3 - 6
-3k = -9
k = -9/-3
k = 3
Hence the value of k is 3
3/4z-1/3=2/3z+1/5