Question

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

Answer 1

Note: I am assuming your second equation is:

x = 2y - 1

Answer:

The solution to the system of equations is:

• x = 1

• y = 1

Explanation:

Given the system of equations

2x+y=3

x = 2y - 1

solving the system of equations using the elimination method

`\begin{bmatrix}2x+y=3\\ x=2y-1\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}2x+y=3\\ x-2y=-1\end{bmatrix}`

Multiply x-2y=-1 by2: 2x-4y=-2

`\begin{bmatrix}2x+y=3\\ 2x-4y=-2\end{bmatrix}`

subtracting the equations

`2x-4y=-2`

`-`

`\underline{2x+y=3}`

`-5y=-5`

now solve -5y = -5 for y

`-5y=-5`

Divide both sides by -5

`(-5y)/(-5)=(-5)/(-5)`

Simplify

`y=1`

For 2x+y=3 plug in y=1

`2x+1=3`

subtract 1 from both sides

`2x+1-1=3-1`

Simplify

`2x=2`

Divide both sides by 2

`(2x)/(2)=(2)/(2)`

Simplify

`x=1`

Therefore, the solution to the system of equations is:

• x = 1

• y = 1