Question

one more

Answer 1

Choose the equivalent system of linear equations that will produce the same solution as the one given below.

4x − 2y = 6
2x + y = 5


−4x − 2y = 10
−4y = 4

−4x − 5y = −1
−7y = 5

3x + 2y = 6
7x = 12

4x + 2y = 10
8x = 16

Answer 2

@mathstudent55 @TheSmartOne

Answer 3

Solve the first system of equations.
You can start by eliminating y.
Multiply the second equation by 2 and add it to the first equation.

Answer 4

4x=6+2y

Answer 5

Rewrite the first equation as it is.
Below it, write the 2nd equation multiplied by 2.
Then add the equations.

Original 1st eq. 4x − 2y = 6
2nd eq. multiplied by 2 4x + 2y = 10
Addition of equations 8x = 16

Do you understand it so far?

Answer 6

ok

Answer 7

@mathstudent55

Answer 8

Ok. Now we have 8x = 16
Solve for x.

Answer 9

x=2

Answer 10

Good.
Now we plug in that value of x into either one of the two original equations to find y.

Answer 11

Let's use the second equation:

2x + y = 5

We replace x with 2:

2(2) + y = 5

Can you solve for y?

Answer 12

y=1

Answer 13

Great.
Now we know that the given system of equation has the solution

x = 2 and y = 1

Answer 14

Now we need to see which other system of equations among the choices has the same solution.

Answer 15

ok

Answer 16

In theory, we would have to solve each of the 4 systems of equations and compare solutions, but there is a much faster way.

Answer 17

I think it is D because x =2 and y = 1

Answer 18

Notice that everyone of the 4 choices has one equation (always the second equation) that has only one variable. That equation is very easy to solve.

Start with choice A.
Solve for y:
−4y = 4

Answer 19

You are correct.

Answer 20

How did you find the answer so quickly?

Answer 21

I started from D
lol

Answer 22

Lucky guess.
The way I was showing you was to solve the easy equation of each choice.
If that variable does not match our solution, then you can move on to the next choice.
By starting with the last choice, you found the correct answer in the first try.
Good job!