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Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x,y).3x - 2y = -95x + 10y = - 5

Sagot :

Given,

[tex]\begin{gathered} 3x-2y=-9\ldots\ldots\ldots(1) \\ 5x+10y=-5\ldots\ldots\text{.}(2) \end{gathered}[/tex]

Multiply 1st equation by 5.

[tex]\begin{gathered} 5(3x-2y=-9) \\ 15x-10y=-45\ldots\ldots\text{.}(3) \end{gathered}[/tex]

Solve equations (2) and (3)

[tex]\begin{gathered} 20x=-50 \\ x=\frac{-5}{2} \end{gathered}[/tex]

Put x =-5/2 in equation (1)

[tex]\begin{gathered} 3x-2y=-9 \\ 3\times\frac{-5}{2}-2y=-9 \\ \frac{-15}{2}-2y=-9 \\ -2y=-9+\frac{15}{2} \end{gathered}[/tex]

Further solved as,

[tex]\begin{gathered} -2y=\frac{-45+15}{5} \\ -2y=\frac{-30}{5} \\ -2y=-6 \\ y=3 \end{gathered}[/tex]

Therefore, the value of x and y is -5/2 and 3.