Chapter 9.6, Problem 53E

a.

To determine

To calculate the system of equation using graph

Answer to Problem 53E

  $x=2,-2$ and $y=11,-5$

Explanation of Solution

Given information:

  $\begin{array}{l}y=4x+3\\ y=x^2+4x-1\end{array}$

Graph:

  

Interpretation:

Since the two lines intersect at,

  $(2,11),(-2,-5)$

Hence, the solution of the system of equation is,

  $x=2,-2$ and $y=11,-5$

b.

To determine

To calculate the system of equation using substitution

Answer to Problem 53E

  $x=2,-2$ and $y=11,-5$

Explanation of Solution

Given information:

  $\begin{array}{l}y=4x+3\\ y=x^2+4x-1\end{array}$

Formula used: substitution

Calculation:

Equation 1 is $y=4x+3$

Equation 2 is $y=x^2+4x-1$

Substituting equation 1 to equation 2,

  $4x+3=x^2+4x-1$

Shifting the values,

  $x^2+4x-1-(4x+3)=0$

On solving,

  $x^2-4=0$

Shifting the values,

  $x^2=4$

Square rooting,

  $x=\pm 2$

For +2, value of y, substituting the value in equation 1,

  $4(2)+3$

On solving,

  $11$

For -2, value of y, substituting the value in equation 1,

  $4(-2)+3$

On solving,

  $-5$

Hence, the solution of the system of equation is,

  $x=2,-2$ and $y=11,-5$

c.

To determine

To calculate the system of equation using elimination

Answer to Problem 53E

  $x=2,-2$ and $y=11,-5$

Explanation of Solution

Given information:

  $\begin{array}{l}y=4x+3\\ y=x^2+4x-1\end{array}$

Formula used: elimination

Calculation:

Equation 1 is $y=4x+3$

Equation 2 is $y=x^2+4x-1$

For elimination, subtracting the equations

  $y-y=4x+3-(x^2+4x-1)$

On solving,

  $0=-x^2+4$

So,

  $x^2=4$

Square rooting,

  $x=\pm 2$

For +2, value of y, substituting the value in equation 1,

  $4(2)+3$

On solving,

  $11$

For -2, value of y, substituting the value in equation 1,

  $4(-2)+3$

On solving,

  $-5$

Hence, the solution of the system of equation is,

  $x=2,-2$ and $y=11,-5$