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

Sagot :

absor201

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

[tex]\begin{bmatrix}2x+y=3\\ x=2y-1\end{bmatrix}[/tex]

Arrange equation variables for elimination

[tex]\begin{bmatrix}2x+y=3\\ x-2y=-1\end{bmatrix}[/tex]

Multiply x-2y=-1 by2:     2x-4y=-2

[tex]\begin{bmatrix}2x+y=3\\ 2x-4y=-2\end{bmatrix}[/tex]

subtracting the equations

[tex]2x-4y=-2[/tex]

[tex]-[/tex]

[tex]\underline{2x+y=3}[/tex]

[tex]-5y=-5[/tex]

now solve -5y = -5 for y

[tex]-5y=-5[/tex]

Divide both sides by -5

[tex]\frac{-5y}{-5}=\frac{-5}{-5}[/tex]

Simplify

[tex]y=1[/tex]

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

[tex]2x+1=3[/tex]

subtract 1 from both sides

[tex]2x+1-1=3-1[/tex]

Simplify

[tex]2x=2[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{2}{2}[/tex]

Simplify

[tex]x=1[/tex]

Therefore, the solution to the system of equations is:

  • x = 1
  • y = 1
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