Solve by addition method:?

Question

Solve by addition method:
2x + 5y = -1
2x - y = 2

Answer 1

This one is easier by subtraction, but whatever. In order to use addition to eliminate one of the variables, you have to make sure that the coefficient of one of the variables in one of the equations is the opposite of (that is, the negative of) the coeffiecient of the same variable in the other equation. In this case, multiply the entire second equation by -1 to get:
-2x + y = -2

Add this to the first equation to get:
2x + 5y = -1
+(-2x + y = -2)
-------------------
6y = -3
y = -1/2

Plug this back into one of the equations (the second one looks easier) to get:
2x + 1/2 = 2
2x = 3/2
x = 3/4

Answer 2

1.from second eq: 2x = 2+y
substitute in eq 1:
2+y +5y =-1
=> 6y = -3
=> y =-3/6 = -1/2
hence 2x = 2-1/2 = 3/2 or x = 3/4
2.multiply second eq by 5 and add to first one eliminate y, and solve for x:
12x = 9
x =9/12=3/4
now substitute value of x in 2nd eq:
y = 2x-2 =3/2 - 2 = -1/2
But these are normally called substitution method and i dont find any other way.

Answer 3

With these two equations, I would multiply the bottom one by (-1), because we are trying to get one of the variables to cancel out...
2x + 5y = -1
(-2x) - (-y) = -2 ... or ...

2x + 5y = -1
-2x + y = -2 ... add the equations together...

(2x - 2x) + (5y + y) = ((-1) + (-2)) ... or...

6y = -3 ... divide both sides by 6 ...
y = -½ or -0.5

Now, using either original equation, insert the "y" value where there is a "y":
2x + 5(-½) = -1 ... simplify...
2x + (-(5/2) = -1 ... add (5/2) to both sides...
2x = 3/2 ... divide both sides by 2...
x = ¾

Check your answers with the other equation:
2(¾) - (-½) = 2
(3/2) + ½ = 2
4/2 = 2
2 = 2 ... and the answer checks out.

x = -½ and y = 01¾

Answer 4

1) multiply the first equation by (-1),to cancel out -2x with 2x
so : -2x - 5y =1
2) -5y = 1
-y = 2
-5y -y = -6y , 1+2 =3
so : -6y= 3
y = -1/2 ( divide each side by -6)
now we have to find the value of x :
2x -(-1/2) = 2 ( substitute the value of y in one of the two original eq.)
2x = 1.5 ( subtract 1/2 from both sides)
x = 0.75 ( divide each side by 2)
so the answer is : ( 0.75 , -1/2 )

Answer 5

2x + 5y = -1 multiply by -1: -2x-5y=1
2x - y = 2
-2x-5y=1 add
-6y=3 divide by -3
y=-1/2

substitute
2x-(-1/2)=2
2x=3/2
x=3/4

solution is (3/4, -1/2)

check
2(3/4)+5(-1/2)=-1
3/2-5/2=-1
-2/2=-1

Answer 6

2x + 5y = -1.....Eq 1
2x - y = 2.....Eq 2
Subtract Eq 2 from Eq 1
2x - 2x + 5y -(-y) = -1-2
5y + y = -3
6y = -3
y = -3/6
y = -1/2
Now substitute the value of 'y' in Eq 2
2x - y = 2
2x -(-1/2) = 2
2x + 1/2 = 2
2x = 2 - 1/2
2x = 1 1/2
2x = 3/2
x = 3/(2*2)
x = 3/4
The ordered pair solution is : (3/4, -1/2)

Answer 7

2x + 5y = -1
2x - y = 2
subtract second eq from first
2x + 5y -2x + y =-1- 2
6y=-3
y=-1/2
put in first eq to find x

Answer 8

2x + 10y = 20 -2x + 20 = 10y 10y + 20 = 20 + 10y no solution because everything cancels out the two lines are parallel

Answer 9

(1)+(2)*5
2x+5y=-1
10x-5y=10
12x=9
x=9/12=>3/4
(1)+(2)*-1
2x+5y=-1
-2x+y=-2
6y=-3
y=-1/2

Answer 10

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