Question

Solve each system of equations 2x + 3y = 9 x - 2y = 1 Ordered pair

Answer 1

Given the equation system

`\begin{gathered} 2x+3y=9 \\ x-2y=1 \end{gathered}`

First step is to write of the equations in terms of one of the variables, for example I'll write the second equation in terms of x:

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

Second step is to replace the expression obtained for x in the first equation:

`2(1+2y)+3y=9`

Solve the parentheses using the distributive property of multiplications:

`\begin{gathered} 2\cdot1+2y\cdot2+3y=9 \\ 2+4y+3y=9 \\ 2+7y=9 \end{gathered}`

Pass the 2 tothe other side of the equation by subtracting it from both sides of the = sign

`\begin{gathered} 2-2+7y=9-2 \\ 7y=7 \end{gathered}`

And divide both sides by 7

`\begin{gathered} (7y)/(7)=(7)/(7) \\ y=1 \end{gathered}`

Replace it in the first expression obtained to determine the value of x:

`\begin{gathered} x=1-2y \\ x=1-2\cdot1 \\ x=1-2 \\ x=-1 \end{gathered}`

This sistem of equations has one solution at x=-1 and y=1