Question

Determine algebraically any point(s) of intersection of the graphs of the equations. Verify your results using the intersect feature of a graphing utility. $$\begin{aligned} x+y &=8 \\ -\frac{2}{3} x+y &=6 \end{aligned}$$

Name: Problem 93, Chapter 3: College Algebra: Real Mathematics, Real People
Uploaded: 2020-07-31T05:29:53-08:00
Duration: 1 min 2 s
Channel: Ankit Gupta
Description: Determine algebraically any point(s) of intersection of the graphs of the equations. Verify your results using the intersect feature of a graphing utility. x+y =8 -(2)/(3) x+y =6

   Determine algebraically any point(s) of intersection of the graphs of the equations. Verify your results using the intersect feature of a graphing utility. 
$$\begin{aligned}
x+y &=8 \\
-\frac{2}{3} x+y &=6
\end{aligned}$$

College Algebra: Real Mathematics, Real People

Ron Larson 7th Edition

Chapter 3, Problem 93

Instant Answer

Solved by Expert Ankit Gupta

07/31/2020

Step 1

We can solve the system by substitution or elimination. Let's use the elimination method. To eliminate the y-term, we can multiply the first equation by 3 and the second equation by 2/3: $$\begin{aligned} 3(x+y) &= 3(8) \\ \frac{2}{3}(-\frac{2}{3}x+y) &= Show more…

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Determine algebraically any point(s) of intersection of the graphs of the equations. Verify your results using the intersect feature of a graphing utility. $$\begin{aligned} x+y &=8 \\ -\frac{2}{3} x+y &=6 \end{aligned}$$

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Key Concepts

Graphical Verification

Graphical verification involves plotting the equations on a coordinate grid and identifying the point(s) where the graphs intersect. This visual approach is used to confirm the accuracy of the algebraic solution by ensuring that the calculated intersection point appears on both graphs.

System of Linear Equations

A system of linear equations consists of two or more equations with the same set of variables. The solution to this system is the set of variable values that satisfy each equation simultaneously, which, when graphed, corresponds to the point(s) where the lines intersect.

Elimination Method

The elimination method is a technique used to solve systems of equations by adding or subtracting equations to eliminate one of the variables. This simplifies the system to a single equation in one variable, which can then be solved easily before back-substituting to find the other variable.

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