Math
posted by Vanessa on .
Find the intersection point.
3x+2y = 3
2x+10y = 5
I put them into y=mx+b form and got
y=3/2 + 3/2
y=1/5x  1/2
I can't seem to find the intersection point by graphing it either, since it won't be accurate.

3 x + 2 y = 3 subtract 3 x to both sides
3 x  3 x + 2 y = 3  3 x
2 y = 3  3 x Divide both sides by 2
y = 3 / 2  3 x / 2
2 x + 10 y =  5 Subtract 2 x to both sides
2 x  2 x + 10 y =  5  2 x
10 y =  5  2 x Divide both sides by 10
y =  5 / 10  2 x / 10
y = y
3 / 2  3 x / 2 =  5 / 10  2 x / 10 Multiply both sides by 10
10 * 3 / 2  10 * 3 x / 2 = 10 *  5 / 10  10 * 2 x / 10
30 / 2  30 x / 2 =  50 / 10  20 x / 10
15  15 x =  5  2 x Add 2 x to both sides
15  15 x + 2 x =  5  2 x + 2 x
15  13 x =  5 Subtract 15 to both sides
15  15  13 x =  5  15
 13 x =  20 Divide both sides by  13
x =  20 /  13
x = 20 / 13
3 x + 2 y = 3
3 * 20 / 13 + 2 y = 3
60 / 13 + 2 y = 3
60 / 13 + 2 y = 3 * 13 / 13
60 / 13 + 2 y = 39 / 13 Subtract 60 / 13 to both sides
60 / 13  60 / 13 + 2 y = 39 / 13 + 60 / 13
2 y =  21 / 13 Divide both sides by 2
y = (  21 / 13 ) / 2 =  21 / ( 13 * 2 ) =  21 / 26
OR
2 x + 10 y =  5
2 * 20 / 13 + 10 y =  5
40 / 13 + 10 y =  5 * 13 / 13
40 / 13 + 10 y =  65 / 13 Subtract 40 / 13 to both sides
40 / 13  40 / 30 + 10 y =  65 / 13  40 / 13
10 y =  105 / 13 Divide both sides by 10
y = (  105 / 13 ) / 10 =  105 / ( 13 * 10 ) =  105 / 130 =  5 * 21 / ( 5 * 26 ) =  21 / 26
Solution :
x = 20 / 13 , y =  21 / 26