SOLUTION: Find the coordinates of any points where the line 2x + 3y = 6 and the ellipse 4x^2 + 9y^2 = 36 intersect.

Question 579755: Find the coordinates of any points where the line 2x + 3y = 6 and the ellipse 4x^2 + 9y^2 = 36 intersect.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the coordinates of any points where the line 2x + 3y = 6 and the ellipse 4x^2 + 9y^2 = 36 intersect.
**
2x+3y=6
3y=6-2x
y=2-2x/3
..
4x^2+9y^2=36
sub y in equation
4x^2+9(2-2x/3)^2=36
4x^2+9(4-8x/3+4x^2/9)=36
4x^2+36-24x+4x^2=36
8x^2-24x=0
x^2-3x=0
x(x-3)=0
x=0
y=2-2x/3=2-0=2
or
x=3
y=2-2x/3=2-6/3=2-2=0
..
ans:
Two points of intersection:(0,2) and (3,0)

RELATED QUESTIONS
the ellipse with equation 4x^2 +9y^2 = 36 , 2x+3y =k is tangent to the elipse, find... (answered by lynnlo)

Find the intersection of two ellipse 4x^2+9y^2=36 , 9x^2+4x^2=36 (answered by ikleyn,solver91311)

Find the foci this ellipse equation. Carefully graph the ellipse. Identify the... (answered by richwmiller)

by sketching graphs, find the number of real solutions the system has. 4x^2+9y^2=36... (answered by Alan3354)

The curves y = 2x^3 and y = (2-x)(5x+6) intersect in 3 points. Find the x-coordinates of... (answered by greenestamps)

Find the center, vertices, foci and eccentricity of the ellipse... (answered by ikleyn)

Find the distance of the point (3,4) to the foci of the ellipse whose equation 4x^2 +... (answered by ikleyn)

5x-3y=2 6x+7y=13 plot each question on fully labeled graph use the graph to find the (answered by Alan3354)

PLEASE HELP!!!! I'm having a hard time with this. Find the foci of this ellipse... (answered by josgarithmetic)