Question

Solve the following system of equations using the substitution method . Use the imfity symbol if infinitely many solutions exists or enter dne for no solutions X+4y=-13 and y= -3x-28 Wright your answer as an ordered pair

Answer 1

Solve the following system of equations using the substitution method

`\begin{gathered} x+4y=-13 \\ y=-3x-28 \end{gathered}`

Using substitution method,

`\begin{gathered} x+4y=-13\ldots\ldots\ldots\text{.....}\mathrm{}(1) \\ y=-3x-28\ldots\ldots\ldots\text{.}\mathrm{}..(11) \end{gathered}`

Substitute the value of y in the equation (1)

`\begin{gathered} y=-3x-28 \\ x+4(-3x-28)=-13 \\ x-12x-112=-13 \\ -11x-112=-13 \\ -11x=-13+112 \\ -11x=99 \\ x=(99)/(-11) \\ x=-9 \end{gathered}`

Solve for the value of y using equ(2)

`\begin{gathered} y=-3x-28 \\ y=-3(-9)-28 \\ y=27-28 \\ y=-1 \end{gathered}`

Therefore the solution of the system of equations are

`(x,y)---\longrightarrow(-9,-1)`