# Math-Linear Systems

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Determine the point of intersection.

(a) y = 4x + 6
y = -x + 1

(b) 2x + 5y = 10
x = 10

Please show how to get the point of intersection. thoroughly explain how to get point of intersection.

• Math-Linear Systems -

• Math-Linear Systems -

for (a), one method:
y = 4x + 6
y = -x + 1
For the standard equation, y = mx + b,
m is the slope. If m is the same for both equations, the lines are the same or parallel. If parallel, the will not intersect. This is not the case here. The lines do intersect.

There are two equations with two unknowns.
Solve for x and y.
One method, eliminate y by substitution, giving:
4x + 6 = -x + 1
Solve for x.
Then, substitute that value of x into either equation and solve for y.

• Math-Linear Systems -

thanks

• Math-Linear Systems -

( 1 , 0 ) POI for (a)
( 10 , 2 ) POI for (b)

• Math-Linear Systems -

Checking (a) only, (1, 0) is not correct. To check your answer, substitute the values into either equation.
So, y = 4x + 6
0 = 4(1) + 6
or
0 = 10
which is not equal

• Math-Linear Systems -

The second equation is:
2x + 5y = 10
2(10) + 5(2) = 10
or
20 + 10 = 10
Not correct

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