Question

Solve the following system of equations.
2x+y=3
x=2y-1

Answer 1

The solution is (1,1).

Explanation:

We have given a system of equations.

2x+y = 3 eq(1)

x = 2y-1 eq(2)

We have to find the solution of given system.

Putting eq(2) into eq(1), we have

2(2y-1)+y = 3

4y-2+y = 3

4y+y = 3+2

Adding like terms, we have

5y = 5

y = 1

Putting value of y in eq(2) , we have

x = 2(1)-1

x = 2-1

x = 1

Hence , the solution is (1,1).

Answer 2

`x=1\\y=1\\\\(1,1)`

Explanation:

Apply the method of substitution:

- Substitute
`x=2y-1` into the first equation:

`2(2y-1)+y=3\\4y-2+y=3\\5y=5\\y=1`

- Substitute the value of y into the any of the original equations and solve for x, as you can see below:

`1=2y-1\\2=2y\\y=1`

Then the solution is:

`x=1\\y=1\\\\(1,1)`