Can anyone help me with solving a system by addition?

Question

Solve the system by addition.
–5x + 2y = 10
x – 3y = 11

Answer 1

yeah!

x=11+3y isolate x

-5(11+3y) +2y = 10 substitute "x" from above equation

-55 -15y + 2y = 10 distributive prop

-13y = 10+ 55 isolate "y"

y = -65/13 = 5

y = 5

x- (3*5) = 11 plug "y" back into second equation

x = 11 +15 = 26

x = 26, y = 5

there you go!

Answer 2

-5x + 2y =10 3* (-5x + 2y =10) = -15x + 6y = 30
+ x - 3y = 11 2* ( x - 3y = 11 ) = 2x - 6y = 22
sum to cancel out a variable: -13x = 52
solve: x= -4
substitute x= -4 into equation 1: 2y= 5x + 10
y=5/2x + 5
y= 5/2(-4) + 5
= -5
So, x= -4 and y= -5. This is the right way to do it by addition, although one of the above answers is right, they use substitiution. So, if you want to solve it using addition, use this method.

Answer 3

So, let's find out what x is in the second line:
x - 3y = 11

We're going to ADD "3y" to both sides of the equation:
x - 3y + 3y = 11 + 3y

On the left side, "-3y" and "+3y" cancel each other out:
x + (3y - 3y) = 11 + 3y
x + 0 = 11 + 3y
x = 3y

Next, we're going to put our value for x into the top equation:
-5x + 2y = 10
-5(3y) + 2y = 10

It should be a breeze from here!

Answer 4

we have to find out the value of one of your variables

x-3y = 11
x= 11 + 3y....aha now we know - and can substitute

-5x + 2y = 10 becomes
-5(11 + 3y) + 2y = 10
-55 -15y + 2y = 10
-55 - 13y = 10....add 13y to both sides
-55 = 10 + 13y.....subtract 10 from both
-65 = 13 y.....divide by 13 and you got it from here !

best of luck!

Answer 5

-5x+2y=10
x-3y=11

x=11+3y

-5(11+3y)+2y=10
-55-15y+2y=10
-13y-55=10
-13y-55+55=10+55
-13y=65
-13y/-13=65/-13
y=-5

x-3(-5)=11
x+15=11
x+15-15=11-15
x=-4

Answer 6

tomcat15 is right