Question

The linear system of equations are:
y=3x
y=1/2x + 5

Which ordered pairs is the solution of the system?
A.(0,0)
B.(0,5)
C.(2,6)
D.(6,2)

Plzz help !!

Answer 1

I plotted them but none of the point listed connect both lines.

Answer 2

An ordered pair which is a solution to the system will be an ordered pair which when substituted into ALL of the equations yields nothing but true number sentences.

You have two approaches here, as this is a multiple-choice question. You could actually solve the system of equations and find the answer, or you try the various answer choices and reject the ones which do not work. I'm a big fan of knowing how to actually do the problem, and am happy to help you if you want to work through it.

As an example of testing ordered pairs to see if they are a solution, what if we had answer choice E: (1,3)?

Let's check it:

first equation is \[y =3x\]plug in our prospective solution of \(x=1,y=3\):
\[3=3(1)\]\[3=3\checkmark\]so far, it looks okay! If this was a false number sentence, we could stop checking right now, but as it is true, we have to press onward.
second equation is \[y=\frac{1}{2}x+5\]
\[3=\frac{1}{2}(1)+5\]\[3=\frac{1}{2}+5\]I hope you agree that equation is not true. That means that \((1,3)\) is not a solution to the system of equations.

Notice that our prospective solution DID satisfy one of the equations. This is an example of why you must check your solution in ALL of the equations.

Answer 3

Are you sure about your work?

Answer 4

@whpalmer4 so I'll try each answer choices and see which one is the solution to the system right now

Answer 5

@rainey_the_blondie I think you might have made an error in plotting the second equation, if I had to guess...

the solution to this system is definitely among the choices offered.

Answer 6

@rainey_the_blondie offers another way to find the solution, which is to plot the two lines and see if/where they intersect. If all of the lines described by the systems of an equation intersect at the same point, that point is a solution to the system.

Answer 7

@whpalmer4 i think its (2,6)

Answer 8

Also, I was given a graph and 2,6 is the intersecting points in the graph

Answer 9

Let's verify:

\[y=3x\]\[6=3(2)\]\[6=6\checkmark\]\[y=\frac{1}{2}x+5\]\[6=\frac{1}{2}(2)+5\]\[6=1+5\]\[6=6\checkmark\]Everything looks good!

Answer 10

Alrighty thank you soooo much !!!! @whpalmer4

Answer 11

Would you like an example of solving it without testing or graph?

\[y=3x\]\[y=\frac{1}{2}x+5\]We have an expression for one of the variables \(y\) in terms of the other \(x\), so we can just substitute that.

\[y= \frac{1}{2}x+5\]\[(3x)=\frac{1}{2}x+5\]multiply both sides by 2 to get rid of the pesky fraction
\[2*3x=2*\frac{1}{2}x+2*5\]\[6x=x+10\]\[6x-x = x-x+10\]\[5x=10\]\[x=2\]now we plug \(x=2\) into one of the original equations:
\[y=3x = 3(2) = 6\]
test in the other equation and you're done.

Answer 12

I don't know if you have covered that yet in your class; it is called solving by substitution. There is another common method called solving by elimination.

Answer 13

I rather doing it with the graph because I'm able to have a full Visualization of what's going on

Answer 14

Oh, it's good to understand it from the graph, I agree, but eventually you want to be able to do it algebraically because graphing may not give you an exact answer, and gets rather tedious as you have more and more equations. Knowing how to do it multiple ways allows you to select the most convenient one for the problem when you have enough experience.

Answer 15

Yeah I agree with you 100% but once thanks for your help really appreciated it :) XD

Answer 16

*ONCE AGAIN

Answer 17

you're welcome!