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lions [1.4K]
3 years ago
7

Pilar says that two linear systems below have the same solution. (see picture) Is she correct? Explain.

Mathematics
2 answers:
Kruka [31]3 years ago
6 0

Answer:

<h2>Pilar is correct because both system of equations are satisfied by the same solution.</h2>

Step-by-step explanation:

To know if both systems have the same solutions we need to solve one of them, and then evaluate that solution with the other system.

Let's solve the first system

3x+2y=2\\5x+4y=6

First, let's multiply the first equation by -2, then we sum both equations each other

-6x-4y=-4\\5x+4y=6

-x=2\\x=-2

Then, we use this value to find the other one

3x+2y=2\\3(-2)+2y=2\\-6+2y=2\\2y=2+6\\y=\frac{8}{2}\\ y=4

Therefore, the solution of the first system of equations is (-2,4).

Now, let's evaluate this values in the second equation and see if they satisfy

3x+2y=2\\3(-2)+2(4)=2\\-6+8=2\\2=2

They satisfy the first equation, let's evaluate the second one

11x+8y=10\\11(-2)+8(4)=10\\-22+32=10\\10=10

They also satisfy the second equation. That means both system have the same solution.

Therefore, Pilar is correct because both system of equations are satisfied by the same solution.

wariber [46]3 years ago
5 0
The first set:

3x + 2y = 2  ---1)
5x + 4y = 6  ---2)

From 1), multiply all by 2, 6x + 4y = 4  ---3)

3) - 2),

6x + 4y - (5x + 4y) = 6 - 4
6x + 4y - 5x - 4y = 2
x = 2

Sub in x = 2 into 1),

3(2) + 2y = 2
2y = -4
y = -2

(2 , -2)


The second set:

3x + 2y = 2  ---1)
11x + 8y = 10  ---2)

From 1), multiply all by 4, 12x + 8y = 8 ---3)

3) - 2),

12x + 8y - (11x + 8y) = 8 - 10
12x + 8y - 11x - 8y = -2
x = -2

From this x value alone, we can tell that these two linear systems do NOT have the same solution as they meet at different coordinates.

Hope this helped! Ask me if there's any working from here that you don't understand! :)

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