Match the system of equations to their solutions

Mathematics

1 answer:

I am Lyosha [343]3 years ago

6 0

Answer:

2x + y = 12 & x = 9 - 2y --- (x = 5, y = 2)

x + 3y = 16 & 2x - y = 11 --- (x = 7, y = 3)

y = 11 - 2x & 4x - 3y = -13 --- (x = 2, y = 7)

2x + y = 11 & x - 2y = -7 --- (x = 3, y = 5)

Step-by-step explanation:

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Find the coordinates of the missing endpoint if P is the midpoint of Line Segment NQ.

dimaraw [331]

Midpoint formula is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ .

So starting with this one, we will be solving for the coordinates of the unknown endpoint separately. Starting with the x-coordinate, since we know that the midpoint x-coordinate is 5 and the x-coordinate of N is 2, our equation is set up as such: $\frac{x+2}{2}=5$ From here we can solve for the x-coordinate of Q.

Firstly, multiply both sides by 2: $x+2=10$

Next, subtract both sides by 2 and your x-coordinate is $x=8$

With finding the y-coordinate, it's a similar process as with the x-coordinate except that we are using the y-coordinates of the midpoint and endpoint N.

$\frac{y+0}{2}=2\\ y=4$