Question

The coordinates below represent two linear equations. How many solutions does this system of equations have?

Line 1
x y
–4 8
4 6
Line 2
x y
–1 1
3 5


A.
0

B.
exactly 1

C.
exactly 2

D.
infinitely many

Answer 1

@pooja195

Answer 2

Okay.

In this problem we are trying to find an equation of form \(y=ax+b\), where \(a\) is slope, and \(b\) is intercept, which passes through points \((x1, y1) = (-4, 8)\) and \((x2, y2) = (4, 6)\)

Answer 3

So, slope \(a\) is:

\[a = \frac{ y2 - y1 }{ x2 - x1 } = \frac{ 6 - 8 }{ 4 - (-4) } = -0.25\]

Answer 4

The intercept is found from this equation: \(a*x1+b = y1\) or also... \(-0.25 * (-4) + b = 7\)

Answer 5

so d

Answer 6

Nope... lets try and solve then I can help you out :)

Answer 7

So, lets find intercept b

Answer 8

We would find this by \(b = y1 - a * x1\) or also \(b = 8 - (-0.25) * (-4) = 7\)

Answer 9

So the equation is \(y = (-0.25)x + 7\)

Answer 10

Now thats for line 1. Lets do line 2 okay? :)

Answer 11

So... now line 2...

Slope \(a\) is \(1\) after solving the same way as we did for line 1.

Intercept \(b\) is \(2\) solving the same way... once again.

So your equation is \(y = 1x + 2\)

Answer 12

so b

Answer 13

Now solve for \(x\). You get 4 and for \(y\) you get 6.

When you graph the two lines they are intersecting at point \((4, 6)\).

Right! So it is B!

Answer 14

Awesome Job! :)

Answer 15

thanks

Answer 16

No problem!

@michelleball477

Answer 17

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