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Chapter 7: Problem 7

Solve each system by graphing. Check the coordinates of the intersection point in both equations. \(\left\\{\begin{array}{l}2 x-3 y=6 \\ 4 x+3 y=12\end{array}\right.\)

Short Answer

Expert verified
After analyzing and following all the steps, plot the lines and find the intersection point. Then validate the values obtained by substitifying these values into the original equations.

Step by step solution

01

Convert to slope-intercept form

To convert to slope-intercept form, we need to solve each equation for 'y'. First equation will transform into \(y = \frac{2x - 6}{3}\) and the second equation will become \(y = \frac{12 - 4x}{3}\).
02

Graph each line

Plot each equation on the same graph. Carefully choose the range of 'x' and use the equations to calculate the corresponding 'y' values. The lines will cross on a point that will be the solution.
03

Determine the solution

Look at the graph and figure out the point of intersection of the two lines. This point (x, y) represents the common solution of the system.
04

Check the solution

Substitute the values of 'x' and 'y' into the original set of equations to verify the solution. If both equations are satisfied, then the solution is correct.

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Most popular questions from this chapter

Use a table of coordinates to graph each exponential function. Begin by selecting \(-2,-1,0,1\), and 2 for \(x\). \(f(x)=5^{x}\)

a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(y=-x^{2}+4 x-3\)

Compare the graphs of \(3 x-2 y>6\) and \(3 x-2 y \leq 6\). Discuss similarities and differences between the graphs.

Graph each linear inequality. \(x \leq 2\)

Without graphing, Determine if each system has no solution or infinitely many solutions. \(\left\\{\begin{array}{l}3 x+y \leq 9 \\ 3 x+y \geq 9\end{array}\right.\)
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