Q53. - 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.

 $\begin{array}{c}3.6x-2y=4\\ -2.7x+y=3\end{array}$

Step-by-Step Solution

Answer

The solution of system of equations is $\left(-5.556,-12\right)$.

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 $3.6x-2y=4$. 

Rewrite the equation in form of slope-intercept form.

Subtract $3.6x$ from both the sides.

$\begin{array}{c}3.6x-2y-3.6x=4-3.6x\\ -2y=4-3.6x\end{array}$

Divide both sides by $-2$.

$y=-2+1.8x$

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

Now, consider the second equation $-2.7x+y=3$. 

Add the term $-2.7x$ on both the sides.

$\begin{array}{c}-2.7x+y+2.7x=3+2.7x\\ y=3+2.7x\\ y=2.7x+3\end{array}$

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 $y=-2+1.8x$ and $y=2.7x+3$

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

Secondly, press the  2^nd key, followed by TRACE key.

Now, select the Intersection option from the list and press ENTER key.

With help of arrow keys move to point of intersection.

Press ENTER key when there is a prompt for first function, press ENTER key when there is a prompt for second function.

Now, for the Guess, press the ENTER key.

Result obtained on screen is provided below:

The intersection point is $\left(-5.556,-12\right)$.

Step-4 – Verify that point satisfies system of equations

The point of intersection is solution of system of equations if the point satisfies both the equation.

Substitute the point $\left(-5.556,-12\right)$ in the equation $3.6x-2y=4$.

Substitute x as $-5.556$ and y as $-12$ and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}3.6\left(-5.556\right)-2\left(-12\right)=4\\ 4=4\end{array}$

Since, this is true so the point $\left(-5.556,-12\right)$ satisfy the equation $3.6x-2y=4$.

Substitute the point $\left(-5.556,-12\right)$ in the equation $-2.7x+y=3$.

Substitute x as $-5.55$ and y as $-12$and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}-2.7\left(-5.556\right)+\left(-12\right)=3\\ 3=3\end{array}$

Since, this is true so the point $\left(-5.556,-12\right)$ satisfy the equation $-2.7x+y=3$.

Hence, the solution of the system of equations is $\left(-5.556,-12\right)$.