Question

Using substitution to solve system of equations:The system of equations below represents the perimeter and length of a rectangular figure, where x represents the width (in meters) of the figure, and y represents the length (in meters). Y=4x+3 2x+2y=351Solve the system of equations, and then find the dimensions

Answer 1

SOLUTION:

We want to use substitution to solve the system of equations;

$\begin{gathered} y=4x+3---i \\ 2x+2y=351---ii \end{gathered}$

Since equation i is given in terms of y explicitly, we can substitute this directly into equation ii;

When we do this, we have;

$\begin{gathered} 2x+2(4x+3)=351 \\ 2x+8x+6=351 \\ 10x=345 \\ x=34.5 \end{gathered}$

Inserting this into equation i, we have;

$\begin{gathered} y=4(34.5)+3 \\ y=141 \end{gathered}$

Thus, the dimensions of the equation are;

x = 34.5 meters and y = 141 meters