Question

A system of equations is shown below:

4x = - 3y + 17
3x - 4y = - 6

What is the solution to this system of equations?

A (-2, -3)

B (3, 2)

C (2, 3)

D (-3, -2)

Answer 1

can someone help me please

Answer 2

Do you know about any of the methods that are used to solve these types of equations?

Answer 3

no I dont

Answer 4

can you help me @Concentrationalizing

Answer 5

Gah, my message got erased *kicks* Alright, well let's try to solve this by the substitution method and hopefully it'll make sense. There are 3 methods, substitution, elimination, and graphing, although graphing is tedious.

So for the substitution method, we want to isolate x or y in any of the 2 equations. If I were to isolate x in the top equation, for example, I could so by simply dividing both sides by 4:
\[4x = -3y + 17 \implies \frac{4x}{4} = \frac{-3y}{4} + \frac{17}{4} \implies x = \frac{-3y}{4} + \frac{17}{4}\]
With x = -3y/4 + 17/4, we can substitute this value for x into the 2nd equation. So Ill replace x in the 2nd equation with an empty space and fill in this equation for x I just found.
\[3x-4y = -6 \implies 3(\frac{-3y}{4}+\frac{17}{4}) - 4y = -6\]I'll clean this up a little bit:

\[\frac{-9y}{4}+\frac{51}{4}-4y = -6\]

Now, having the fractions in there is no fun, so it is best to get rid of them. In order to get rid of them, I can find a common denominator between all the fractions in the equation and multiply EVERY term by this common denominator. In this case the common denominator is easy, just 4. So if I multiply everything by 4 Ill have:

\[4*(\frac{ -9y }{ 4 })+4*(\frac{ 51 }{ 4 })-4*4y= 4*-6 \implies -9y + 51 - 16y = -24\]
Unfortunately I have to leave, but this is the main idea. From here, you need to solve this resultant equation for y. Once you find your y -value, plug it into any of the equations we started with and solve for x. Good luck ^_^