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

Solution

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)

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

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

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