SOLUTION: Can this system by solved by substitution? 6x + 7y = -9 -4x - 5y = 5

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Question 1113803: Can this system by solved by substitution?
6x + 7y = -9
-4x - 5y = 5
Found 3 solutions by math_helper, amalm06, MathTherapy:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Sure!
Solve the first eq for x: x = (-9 - 7y) / 6
Substitute the RHS of this for 'x' in the 2nd eq:

36 + 28y - 30y = 30
-2y = -6
y = 3 —> x = (-9 - 21)/6 = -5
————
Ans: ,
————

Check:
(1) 6x + 7y = 6(-5) + 7(3) = -30 + 21 = -9 (ok)
(2) -4x - 5y = -4(-5) - 5(3) = 20 - 15 = 5 (ok)

Answer by amalm06(224)   (Show Source): You can put this solution on YOUR website!
Yes, x=-5 and y=3. Express x in terms of y (or vice-versa) in the first equation and then solve for y (or x) in the second equation.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Can this system by solved by substitution?
6x + 7y = -9
-4x - 5y = 5
You don't have to deal with ANNOYING fractions by solving for a variable right away. IGNORE anyone who tells you to do that.

In this particular case, ADD the 2 equations to get eq (iii) in the form of: 2x + 2y = - 4

Reduce eq (iii) by dividing it by 2 to get: x + y = - 2____x = - 2 - y

Now, substitute this value for x in any of the 2 equations. I chose eq (ii), and got: - 4(- 2 - y) - 5y = 5

8 + 4y - 5y = 5

4y - 5y = 5 - 8

- y = - 3

 

You then substitute 3 for y in any of the original equations to get x. I chose eq (ii), and got: - 4x - 5(3) = 5

- 4x - 15 = 5

- 4x = 20

 

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