Q55. - Algebra 2

Question

To use a TI-83 Plus to solve a system of equations, graph both equations on the same screen. Then, select intersect, which is option 5 under the CALC menu, to find the coordinates of the point of intersection. Solve each system of equations to the nearest hundredth.

 

 $\begin{array}{c}55.\text{ 1}.6x+3.2y=8\\ 1.2x+2.4y=4\end{array}$

Step-by-Step Solution

Answer

The solution of system of equations is $\varnothing$.

Step-1 – Apply the concept of slope-intercept form

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Step-2 –Write the equations in slope-intercept form

Consider the first equation $1.6x+3.2y=8$. 

Rewrite the equation in form of slope-intercept form.

Subtract $1.6x$ from both the sides.

$\begin{array}{c}1.6x+3.2y-1.6x=8-1.6x\\ 3.2y=8-1.6x\end{array}$

Divide both sides by $3.2$.

$\begin{array}{c}y=2.5-0.5x\\ y=-0.5x+2.5\end{array}$

Now, the equation is in the form $y=mx+c$. 

Now, consider the second equation $1.2x+2.4y=4$. 

Subtract $1.2x$ from both the sides.

$\begin{array}{c}1.2x+2.4y-1.2x=4-1.2x\\ 2.4y=4-1.2x\end{array}$

Divide both sides by $2.4$.

$\begin{array}{c}y=1.66-0.5x\\ y=-0.5x+1.66\end{array}$

Now, the equation is in the form $y=mx+c$. 

Step-3 – Identify the point of intersection of the equations

Follow the steps to plot the equations  on the same plane on TI-83 Plus calculator.

Enter the equations $y=-0.5x+2.5$ and $y=-0.5x+1.66$

First, press the GRAPH key. Graph obtained on screen is provided below.

The graph of the equations are parallel lines. 

As parallel lines never intersect. So, there is no solution to system of equation.

Hence, the solution to system of equations is $\varnothing$.