Solve the following system of equations by substitution: 5x-y= 5 and -x+3y=13.
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To solve a set of equations:
a1*x + b1*y = c1 ...(1)
a2*x + b2*y = c2 ...(2)
by substitution, we express one of the variables in any one of the equations in terms of the other.
For example from (1), we get x = (c1 - b1*y)/a1
This value of x is substituted in (2)
a2*(c1 - b1*y)/a1 + b2*y = c2
=> a2*c1/a1 - (a2*b1/a1)*y + b2*y = c2
=> y(b2 - a2*b1/a1) = c2 - a2*c1/a1
=> y = (c2 - a2*c1/a1)/(b2 - a2*b1/a1)
Obtain the value of y and use it to find x.
For the set of equations that you have to solve:
5x - y = 5 ...(1)
-x + 3y = 13 ...(2)
From (1), y = 5x - 5
Substitute this in (2)
=> -x + 3(5x - 5) = 13
=> -x + 15x - 15 = 13
=> 14x = 28
=> x = 2
As y = 5x - 5 = 10 - 5 = 5
The solution is x = 2 and y = 5