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Given that m=(2,-7) and n =(5,1) solve the following vector equation @ xm+yn=(22,-3) ?
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Mar 11
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Given that m=(2,-7) and n =(5,1) solve the following vector equation @ xm+yn=(22,-3) ?
Equal Vectors
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Mar 11
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To solve the vector equation xm + yn = (22, -3), we need to find the values of x and y that satisfy the equation.
Given that m = (2, -7) and n = (5, 1), we can substitute these values into the equation:
x(2, -7) + y(5, 1) = (22, -3)
Expanding the equation, we get:
(2x, -7x) + (5y, y) = (22, -3)
Now, we can separate the components of the vectors:
2x + 5y = 22
-7x + y = -3
Now, we have a system of two equations with two variables. We can solve this system using any method, such as substitution or elimination.
From the first equation, we can solve for y:
y = (22 - 2x) / 5
Now, we can substitute this expression for y into the second equation:
-7x + (22 - 2x) / 5 = -3
Multiplying by 5 to get rid of the fraction:
-35x + 22 - 2x = -15
Combining like terms:
-37x = -37
Dividing by -37:
x = 1
Now, we can substitute x = 1 back into the first equation to solve for y:
2(1) + 5y = 22
2 + 5y = 22
5y = 20
y = 4
Therefore, the solution to the vector equation xm + yn = (22, -3) is x = 1 and y = 4.
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