Question

Solve by the linear combination method (with or without multiplication).

6x – 2y = 2
–3x + 4y = 5




(1, 2)



(1, 3)



(2, 3)




(1, –2)

Answer 1

(1,2)

Answer 2

Hint:
I multiply the first equation by \(2\), so I get this:
\[\left\{ \begin{gathered}
12x - 4y = 4 \hfill \\
\hfill \\
- 3x + 4y = 5 \hfill \\
\end{gathered} \right.\]

Answer 3

Now, please add such equations together, what do you get?

Answer 4

i still don't get it

Answer 5

If I add such equations together, I can write this:
\[12x - 4y - 3x + 4y = 4 + 5\]
and after a simplification, I get:
\(9x=9\)
next I divide both sides by \(9\):
\[\frac{{9x}}{9} = \frac{9}{9}\]
please simplify

Answer 6

its 1

Answer 7

that's right! we get \(x=1\)

Answer 8

now, if I replace \(x=1\) into your first original equation, I get:
\[6 \cdot \left( 1 \right) - 2y = 2\]
please solve for \(y\)

Answer 9

hint:
after a simple computation, I get:
\(6-2y=2\)

Answer 10

its 4

Answer 11

I'm sorry, it is not \(y=4\)
Hint:
next I add \(-6\) to both sides, so I get:
\[6 - 2y - 6 = 2 - 6\]

Answer 12

after a simplification I can write:
\(-2y=-4\)
then I divide both sides by \(-2\):
\[\frac{{ - 2y}}{2} = \frac{{ - 4}}{2}\]
please simplify

Answer 13

2

Answer 14

oops.. I meant:
\[\frac{{ - 2y}}{{ - 2}} = \frac{{ - 4}}{{ - 2}}\]
That's right! we have \(y=2\)

Answer 15

so, what is the right option?

Answer 16

please keep in mind that the solution is given by the ordered pair \((1,2)\)