Chapter SH, Problem 3.2EP

To determine

To find: the solution of the given system of equation using substitution.

Answer to Problem 3.2EP

  $x=-2;y=-2$ .

Explanation of Solution

Given:

The given system of equation is $\begin{array}{l}y=3x+4\\ y=-2x-6\end{array}$ .

Concept used:

Guidelines for solving system of equation using substitution:

1. Find the value of one unknown expression by using another expression in first equation.
2. Substitutes the value of obtained unknown expression in second equation.
3. Now substitutes the value of any one expression in another expression.

Calculation:

Since the given system of equation is $\begin{array}{l}y=3x+4\\ y=-2x-6\end{array}$ .

Therefore, the value of one unknown expression by using another expression is

  $\begin{array}{l}3x+4=-2x-6\left\{\text{both equal to }y\right\}\\ 3x+4+2x-4=-2x-6+2x-4\left\{\text{add}2x\text{and subtract 4 from both the sides}\right\}\\ 5x=-10\left\{\text{simplify}\right\}\\ x=\frac{-10}{5}\left\{dividebothsidesby5\right\}\\ \therefore x=-2\end{array}$

Now, substitutes the value of x in 1st equation, then:

  $\begin{array}{l}y=3x+4\\ y=3\left(-2\right)+4\left\{\text{substitutes the value of }x\right\}\\ y=-6+4\{\text{multiply}}\\ y=-2\{simplify\text{}}\end{array}$

Hence, the value of given system of equation is $x=-2;y=-2$ .