SOLUTION: 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 fraction

Question 1131020: 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.
{7x+8y=−18
7x+5y=−6
so I first isolated y on the first equation, getting (-7x-18)/8. then i substituted it for y in the second equation getting x=-3.
I then substituted -3 for x on the first and second equation getting 3/8 and -3.
I dont know what I'm doing, if I'm doing it right and if it is a dependent system inconsistent or only one solution. Please help if you can, Thank You!
Found 3 solutions by MathLover1, stanbon, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

......eq.1
......eq.2
----------------------------------
-> so far you did it correctly

.....both sides multiply by

go back to , substitute for

so, system does have solution and it is: and

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
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.
{7x+8y=−18
7x+5y=−6
so I first isolated y on the first equation, getting (-7x-18)/8. then i substituted it for y in the second equation getting x=-3.
I then substituted -3 for x on the first and second equation getting 3/8 and -3.
I dont know what I'm doing, if I'm doing it right and if it is a dependent system inconsistent or only one solution. Please help if you can, Thank You!
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Your single solution should be x = 2; y = -4. It has only one solution.
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Note: Each equation graphs as a line.
If the lines intersect the system has only one solution.
If the lines are parallel the system is inconsistent and there are no solutions.
If the lines are the same line the system is dependent and there are
infinite solutions.
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Cheers,
Stan H.
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Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

Let me show to you much MORE REASONABLE way to solve it by the Substitution method.

7x + 8y = -18 (1) 7x + 5y = -6 (2) The term " 7x " is in the first and in the second equation. Therefore, it is TOTALLY ENOUGH to express 7x from the first equation as 7x = -18 - 8y and then substitute it into the second equation, replacing " 7x " there. You will get then (-18-8y) + 5y = -6 -18 - 8y + 5y = -6 -3y = -6 + 18 = 12 y = = -4. Now substitute this value y= -4 into equation (2) to get 7x + 5*(-4) = -6 7x - 20 = -6 7x = -6 + 20 = 14 x = 14/7 = 2. Answer. The solution is x= 2, y= -4. Check the solution on your own by substituting the found values in the given equations.

Solved.

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By doing in this way, you avoid working with fractions and denominators.

Less computing - less chance to make an error.

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