Math-Linear Systems

posted by .

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 -

    can someone answer this?

  • 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
    substituting your (1,0) answer...
    0 = 4(1) + 6
    or
    0 = 10
    which is not equal

  • Math-Linear Systems -

    A quick check of your answer for b shows a problem.
    The second equation is:
    2x + 5y = 10
    Substituting the answer (10,2)...
    2(10) + 5(2) = 10
    or
    20 + 10 = 10
    Not correct

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc problem

    Consider the function y=(kx)/(x-k) a. Show that y is symmetric with respect to the line y=x. b. Write the equations of the horizontal and vertical asymptotes of y. c. Find the point(s) of intersection of y with the line x-y=-2k, and …
  2. Vectors

    I am really lost and confused! Consider the lines r = (1,-1,1) + t(3,2,1) and r = (-2,-3,0) + u(1,2,3). a) Find their point of intersection. b) Find a vector equation for the line perpendicular to both of the given lines that passes …
  3. Anonymous

    Give the exact intersection point for the equations f(x)=4sin^2x+7sinx+6 and g(x)=2cos^2x-4sinx+11 Ok, my result is that there is no intersection point because if you put f(x)=g(x) and try to solve for x or the intersection point, …
  4. Math

    Find the point of intersection between y=2-(1/2)x and y=1+ax. (a=alpha sign). You answer will be a point in the xy plane whose coordinates involve the unknown a . I got that which is x=2/(2a+1), y=(1+2a)/(2a+1) <-intersection point …
  5. Calculus

    The graphs of f(x) = x^3 and g(x) = 3X+5 have one intersection point. Determine the x-value for this intersection point using Newton's Method with an initial estimate of X1=2. You should use this method three times in order to obtain …
  6. calculus

    the graphs of f(x0=x^3 and g(x)=3x+5 have one intersection point. Determine the x-value for this intersection point using Newton's Method with an initial estimate of x1+2. You should use this method 3 times in order to obtain estimates …
  7. Calculus

    Explain fully please and thank you! =) Determine the point of intersection of the lines L1: r= (1,3,7) + s(1,2,-2),seR and L2: v=(0,2,-3) +t(1,1,4), teR. a) P(1,3,1) b P(1,3,7) c) The lines coincide d) no point of intersection
  8. calculus

    Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 429 knots (nautical miles per hour; a nautical …
  9. Calc

    Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 427 knots (nautical miles per hour; a nautical …
  10. Calc

    Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 427 knots (nautical miles per hour; a nautical …

More Similar Questions