To calculate: The solution for the system of equations 7\left(x-y\r

xcl3411 2021-11-15 Answered
To calculate: The solution for the system of equations \(\displaystyle{7}{\left({x}-{y}\right)}={3}-{5}{x}\) and \(\displaystyle{4}{\left({3}{x}-{y}\right)}=-{2}{x}\), if the system does not have one unique solution, state whether the system is inconsistent, or whether the equations are dependent

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Ryan Willis
Answered 2021-11-16 Author has 7145 answers

Given Information:
The provided system of equations is \(\displaystyle{7}{\left({x}-{y}\right)}={3}-{5}{x}\) and \(\displaystyle{4}{\left({3}{x}-{y}\right)}=-{2}{x}\).
Formula used:
Solving a System of Equations by Using the Addition Method:
Step1: Write both equations in standard form: \(\displaystyle{A}{x}+{B}{y}={C}\)
Step2: Clear fractions or decimals.
Step3: Multiply one or both equations by nonzero constants to create
opposite coefficients for one of the variables.
Step4: Add the equations from step3 to eliminate one variable.
Step5: Solve for the remaining variable.
Step6: Substitute the known value found in step5 into one of the original equations to solve for the other variable.
Step7: Check the ordered pair in each equation and write the solution set.
Calculation:
Consider the provided system of equations, \(\displaystyle{7}{\left({x}-{y}\right)}={3}-{5}{x}\) and \(\displaystyle{4}{\left({3}{x}-{y}\right)}=-{2}{x}\)
Convert the equations into standard form \(\displaystyle{A}{x}+{B}{y}={C}\):
\(\displaystyle{7}{\left({x}-{y}\right)}={3}-{5}{x}\)
\(\displaystyle{7}{x}-{7}{y}={3}-{5}{x}\) ............(1)
\(\displaystyle{7}{x}-{2}{y}={3}\)
And,
\(\displaystyle{4}{\left({3}{x}-{y}\right)}=-{2}{x}\)
\(\displaystyle{12}{x}-{4}{y}=-{2}{x}\)............(2)
\(\displaystyle{14}{x}-{4}{y}=-{0}\)
Now, multiply by —2 in the equation (1):
\(-14x+4y=-6\)............(3)
Now, add equations (2) and (3):
\(\displaystyle{14}{x}—{4}{y}={0}\)
\(\displaystyle-{l}{4}{x}+{\left.{d}{y}\right.}=-{6}\)
\(\displaystyle\overline{{{0}=-{6}}}\)
The system of equations is reduced to a contradiction. Hence, the system is inconsistent.
Therefore, the solution for the system of equations \(\displaystyle{7}{\left({x}-{y}\right)}={3}-{5}{x}\) yand \(\displaystyle{4}{\left({3}{x}-{y}\right)}=-{2}{x}\) is {} and the system is inconsistent.

Not exactly what you’re looking for?
Ask My Question
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-11-12
To calculate: The solution for the system of equations \(\displaystyle{5}{x}^{{{2}}}+{y}^{{{2}}}={14}\) and \(\displaystyle{x}^{{{2}}}-{2}{y}^{{{2}}}=-{17}\). If the system does not have a unique solution, determine whether the system is inconsistent, or the equations are dependent.
asked 2021-11-17
To calculate: The solution for the system of equations
\(\displaystyle-{2}{x}^{{{2}}}+{3}{y}^{{{2}}}={10}\);
\(\displaystyle{5}{x}^{{{2}}}+{2}{y}^{{{2}}}={13}\).
asked 2021-11-17
To calculate: The solution for the system of provided equations:
\(\displaystyle{5}{a}-{2}{b}+{3}{c}={10}\)
\(\displaystyle-{3}{a}+{b}-{2}{c}=-{7}\)
\(\displaystyle{a}+{4}{b}-{4}{c}=-{3}\)
asked 2021-11-15
To calculate: The solution for the system of equations \(\displaystyle{0.2}{x}={0.35}{y}-{2.5}\) and \(\displaystyle{0.16}{x}+{0.5}{y}={5.8}\), if the system does not have one unique solution, state whether the system is inconsistent, or whether the equations are dependent.
asked 2021-11-15
To calculate: The solution for the system of equations \(\displaystyle{2}{x}^{{{2}}}-{x}{y}={24}\) and \(\displaystyle{x}^{{{2}}}+{3}{x}{y}=-{9}\)
asked 2021-11-17
To calculate: The solution of the equation \(\displaystyle{x}^{{{2}}}-{5}={\left({x}+{2}\right)}{\left({x}-{4}\right)}\).
asked 2021-11-14
\(\displaystyle{x}+{2}{y}+{z}={5}\) To calculate: The solution for the system of equation \(\displaystyle{x}+{y}-{z}={1}\)
\(\displaystyle{4}{x}+{7}{y}+{2}{z}={16}\)
and if the system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
...