# Math

posted by 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.

• Math - ,

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