-3x+10y=23 and 5x+2y=55 I need to solve this linear system by using elimination.

Question

I don't know how to solve it. Can you please help me? I have to do 20 problems like this. Can someone please show me how to solve this problem so I know how to do all the rest? I'm confused at what to do.

Answer 1

 

Elimination method:
-3x+10y=23 ------------ (1)
5x+2y=55 --------------- (2)

multiply the equation (2) by 5.
25x+10y=275 ---------- (3)

Eliminate the variable y by subtracting equation 1 from equation 3.

25x + 10y = 275
-3x + 10y = 23

28x = 252

divide each side by 28
28x /28 = 252/28
x = 9

substitute x =9 in equation 2

5 * 9 + 2y = 55
45 + 2y = 55

subtract 45 from each side
2y = 55 -45 = 10

divide each side by 2
y = 10/2 = 5

(x, y) = (9, 5)