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Chapter 7: Problem 8

Solve each system by graphing. Check the coordinates of the intersection point in both equations. \(\left\\{\begin{array}{l}4 x+y=4 \\ 3 x-y=3\end{array}\right.\)

Short Answer

Expert verified
The solution to the system of equations is \((1,0)\).

Step by step solution

01

Rewrite in slope-intercept form

Start by isolating \(y\) in both equations. The first equation, \(4x + y = 4\) becomes \(y = -4x + 4\). The second equation, \(3x - y = 3\) becomes \(y = 3x - 3\).
02

Plot the lines

On a graph paper, plot the lines \(y = -4x + 4\) and \(y = 3x - 3\). These lines will intersect at the solution point of the system.
03

Find the intersection point

By graphing, the intersection point appears to be \((1, 0)\). This is the solution to the system of equations.
04

Verify the solution

Substitute \((1, 0)\) into both original equations in order to verify. For the first equation, \(4(1) + 0 = 4\) is true. For the second equation, \(3(1) - 0 = 3\) is also true. Hence, the solution to the system is valid.

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