Question 1178173: Solve the following system of equations.
2 x+ 3 y = 4
5 x - 5 y = -15
Answer: (x,y) = Found 3 solutions by mananth, ikleyn, MathLover1:Answer by mananth(16946) (Show Source):
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2 x+ 3 y = 4
5 x - 5 y = -15
10 x 15 y = 20
15 x -15 y = -45
Add the two equations
25 x = -25
/ 25
x = -1
plug value of x in (1)
2 x + 3 y = 4
-2 + 3 y = 4
3 y = 6
y = 2
Ans x = -1
y = 2
The starting equations are
2x + 3y = 4 (1)
5x - 5y = -15 (2)
In equation (2), divide both sides by 5. Keep equation (1) as is. You will get
2x + 3y = 4 (3)
x - y = -3 (4)
Now multiply equation (4) by 3 (both sides). You will get
2x + 3y = 4 (5)
3x - 3y = -9 (6)
Next, add equations (5) and (6). You will get
5x = 4 - 9 = -5
hence, x = -5/5 = -1.
Now find y from equation (4)
y = x + 3 = -1 + 3 = 2.
ANSWER. x= -1; y= 2.
CHECK. Check the solution ON YOUR OWN by substituting the found values to the original equations.
