# What is the solution to the following system of equations? 3x-6y=-12 x-2y=-8 (a)Use the substitution method to justify that the given system of equations has no solution. (b)What do you know about the two lines in this system of equations?

Question
Equations
What is the solution to the following system of equations?
3x-6y=-12
x-2y=-8
(a)Use the substitution method to justify that the given system of equations has no solution.
(b)What do you know about the two lines in this system of equations?

2020-11-04
Part (a)
The given system of equation is
3x−6y=−12
x−2y=−8
Substitute x=−8+2y in 3x−6y=−12 and solve as follows.
3(−8+2y)−6y=−12
−24+6y−6y=−12
−24+0=−12
−24=−12
Thus, there is no solution for the given system of equations.
Part (b)
Look at the system of equations
3x−6y=−12
x−2y=−8.
Rewrite it as x−2y=−4 (divided by 3).
x−2y=−8
Note that two equations differs only by a constant.
Therefore, the given equations are parallel lines.

### Relevant Questions

Use the method of substitution to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
y=-11
x+2y=7
Solve the following system of linear equations in two variables by Substitution method.
x=8-2y
2x+3y=13
Use Gaussian elimination to find the complete solution to the system of given equations, or show that none exists.
$$\displaystyle{\left\lbrace\begin{array}{c} {5}{x}+{8}{y}-{6}{z}={14}\\{3}{x}+{4}{y}-{2}{z}={8}\\{x}+{2}{y}-{2}{z}={3}\end{array}\right.}$$
1. Find each of the requested values for a population with a mean of $$? = 40$$, and a standard deviation of $$? = 8$$ A. What is the z-score corresponding to $$X = 52?$$ B. What is the X value corresponding to $$z = - 0.50?$$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $$M=42$$ for a sample of $$n = 4$$ scores? E. What is the z-scores corresponding to a sample mean of $$M= 42$$ for a sample of $$n = 6$$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $$a. -2.00 b. 1.25 c. 3.50 d. -0.34$$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $$\mu = 78$$ and $$\sigma = 12$$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $$82, 74, 62, 68, 79, 94, 90, 81, 80$$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $$12 (\mu = 42, \sigma = 12)$$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is$44.50 from tips. Test for a difference between this value and the population mean at the $$\alpha = 0.05$$ level of significance.
Fill in the blank/s: When solving x = 3y + 2 and 5x - 15y = 10 by the substitution method, we obtain 10 = 10, so the solution set is ___________ The equations in this system are called ___________ . If you attempt to solve such a system by graphing, you will obtain two lines that ___________
Solve the following system of linear equations in two variables by Substitution method.
x=-2y-2
2x+5y=-7
Solve the following system of linear equations in two variables by Substitution method.
5x-2y=-7
x=-2y+1
When solving systems of equations we have at least two unknowns. A common example of a system of equations is a price problem. For example, Jacob has 60 coins consisting of quarters and dimes.
The coins combined value is \$9.45. Find out how many of each (quarters and dimes) Jacob has.
1.What do the unknowns in this system represent and what are the two equations that that need to be solved?
2.Finally, solve the system of equations.
$$\displaystyle\frac{{1}}{{3}}{x}+{y}=\frac{{5}}{{4}}$$
$$\displaystyle\frac{{2}}{{3}}{x}-\frac{{4}}{{3}}{y}=\frac{{5}}{{3}}$$
Part A: $$\displaystyle\frac{{{W}\hat{\propto}{e}{r}{t}{y}}}{{\propto{e}{r}{t}{i}{e}{s}}}$$ can be used to write an equivalent system?
$$\displaystyle{\left\lbrace\begin{array}{c} {2}{x}-{4}{y}+{z}={3}\\{x}-{3}{y}+{z}={5}\\{3}{x}-{7}{y}+{2}{z}={12}\end{array}\right.}$$