Answer:
The solution to the system of equations is:
x = 2, and y = -1
Explanation:
Given the pair of equations:
4x + 5y = 3 ..........................................................................(1)
2x + 3y = 1............................................................................(2)
To solve this by elimination:
Multiply equation (2) by 2, to eliminate x
Equation (2) becomes
4x + 6y = 2 .........................................................................(3)
Subtract equation (1) from (3)
4x - 4x + 6y - 5y = 2 - 3
y = -1 ....................................................................................(4)
Multiply equation (1) by 3 and equation (2) by 5 to eliminate y
Equation (1) becomes
12x + 15y = 9 .......................................................................(5)
Equation (2) becomes
10x + 15y = 5 ........................................................................(6)
Subtract equation (6) from (5)
12x - 10x + 15y - 15y = 9 - 5
2x = 4
Divide both sides by 2
x = 4/2 = 2 ............................................................................(7)
From equations (7) and (4)
x = 2, and y = -1
1. y=6
2. y=-12
Step-by-step explanation:
<u>1) If y varies inversely as x, and y=3 as x = -2, find y for the x value of -1.</u>
It is given that
y varies inversely as x
IT will be written as:
y∝1/x
Removing the proportionality symbol
y=k/x
Given
y=3 , x=-2
Putting the values
3=k/-2
k=3*-2 = -6
The equation will be:
y=-6/x
So,
When x=-1
<u>2) If y varies directly as x, and y=15 as x=-3, find y for the x value of 4</u>
y is directly proportional to x
y∝x
y=kx
Given
y=15, x=-3
Putting the values
Hence,
1. y=6
2. y=-12
Keywords: Proportion, Variation
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