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

Step-by-step 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

$\frac{-5y}{-5}=\frac{-5}{-5}$

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

$\frac{2x}{2}=\frac{2}{2}$

Simplify

$x=1$

Therefore, the solution to the system of equations is:

• x = 1

• y = 1