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Chapter 7: Problem 69

Explain how to solve a system of equations using the addition method. Use \(3 x+5 y=-2\) and \(2 x+3 y=0\) to illustrate your explanation.

Short Answer

Expert verified
The solutions for the system of equations are \(x=6\) and \(y=-4\).

Step by step solution

01

Prepare the equations for addition

Check if addition of the given equations will eliminate any variable. Here, directly adding the equations will not eliminate any variable. Then we will need to multiply one or both equations by suitable numbers such that the coefficients of one variable become the same, thus facilitating the elimination. Multiply the first equation by 2 and the second by 3. This gives \(6x+10y=-4\) and \(6x+9y=0\).
02

Add the two new equations

After performing the operation above, add these two new equations together : \(6x+10y=-4\) and \(6x+9y=0\). Since the '6x' is the same in both equations, it gets eliminated when you subtract the second equation from the first one to get \(y=-4\). This is the solution for 'y'.
03

Substitute the value of y into one of the original equations

Substitute the obtained value of 'y' into one of the original equations to find the value of 'x'. In the equation \(2x+3y=0\), put -4 instead of y. This gives \(2x-12=0\). Solving this, we get \(x=6\). This is the solution for 'x'.

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Most popular questions from this chapter

In Exercises 7-8, a. Rewrite each equation in exponential form. b. Use a table of coordinates and the exponential form from part (a) to graph each logarithmic function. Begin by selecting \(-2,-1,0,1\), and 2 for \(y\). \(y=\log _{4} x\)

Graph each linear inequality. \(x \geq 0\)

Graph each linear inequality. \(y \geq 0\)

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -3 \\ \hline 1 & -2 \\ \hline 2 & 0 \\ \hline 3 & 4 \\ \hline 4 & 12 \\ \hline \end{array} $$

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x+2 y \leq 4 \\ y \geq x-3\end{array}\right.\)
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