For the following system, use the second equation to make a substitution for y in the first equation.

2x + y = 5

y + 3 = 2x

2 x + 2 x - 3 = 5
2 x + 3 - 2 x = 5
2 x + 2 x + 3 = 5

For the following system, use the second equation to make a substitution for y in the first equation is 2x + ( 2x – 3 ) = 5

Solution:

Given, two equations are 2x + y = 5 ⇒ ( 1 )  

And y + 3 = 2x ⇒ ( 2 )

We have to find the solution of the given system of equations by substituting the y in second equation in the first equation.

Now, let us find the y value in the second equation

Then, eqn (2) ⇒ y + 3 = 2x

⇒ y = 2x – 3  

Now, substitute the y value in ( 1 )

Eqn ( 1 ) ⇒ 2x + ( 2x – 3 ) = 5

⇒ 2x + 2x – 3 = 5  

Thus we have used second equation to make a substitution for y in first equation

⇒ 4x = 5 + 3  

⇒ 4x = 8  

⇒ x = 2

Then, eqn 2 ⇒ y + 3 = 2(2)  

⇒ y + 3 = 4  

⇒ y = 1

Hence, the solution of the given system of equations is (2, 1).

By use the second equation to make a substitution for y in the first equation we get 2x + 2x – 3 = 5  

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answer: 1/6

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