Question

Solve 5x - 6y = -38
3x + 4y = 0 (1 point)
4, 3
-4, 3
4, -3
-4,3

Answer 1

You can use 3 Rules for this type of problem to isolate one variable:
1. Add/subtract the two equations;
2. Solve one equation for x and substitute it for x in the second equation; or
3. Plug each answer choice to deterine which satisfies the equation.

Answer 2

Here, I would use Rule #3-start with (E) and plug in x=-4 and y=3 and see if both equations are satisfied. If not, try choice D, choice C, etc.

Answer 3

Rule #3 is one that should be avoided except in extreme time pressure. In real life, or with an old school teacher, you need to actually, you know, FIND THE ANSWER :-)

Answer 4

\[5x-6y=-38\]\[3x+4y=0\]Neither of those equations looks like it will give a nice expression (no fractions) if solved for either variable, so let's rule out substitution.

Now, what numbers could we multiply the equations by respectively so that one of the variables ends up with coefficients which are equal in magnitude but opposite in sign?
Two possibilities are:
1) multiply first equation by 3, and the second equation by -5. That will give us 15x for the first equation and -15x for the second.

2) multiply the first equation by 2, and the second equation by 3. That will give us -12y for the first equation and 12y for the second.

Let's do the second one:

\[2*5x-2*6y = 2*-38\]\[3*3x+3*4y=3*0\]or\[10x-12y = -76\]\[9x+12y=0\]Now we'll add the two equations together.\[10x+9x-12y+12y=-76+0\]\[19x=-76\]\[x =\]
With our newly found value of \(x\), we back-substitute it into either of the original equations and solve for the value of \(y\).

Answer 5

When you think you have a solution for both \(x\) and \(y\), you need to plug them into both equations and make sure that both equations are satisfied. It is possible to come up with a "solution" which satisfies one equation but not the other. That kind of solution has a special name: "wrong" :-)