# Solve the following system of equations by substitution: 5x-y= 5 and -x+3y=13.

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### 1 Answer

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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**