Question

Solve the following system by the elimination method. Check the solution.
5x−5=−7y , 6x+5y=−11

Answer 1

I assume elimination method is to eliminate one of the variables. in order to eliminate one then that variable must have the same coefficient in both equations. I look at what will be easier to eliminate. The x values look easier with 6 and 5. in order to make them equal I must multiply each equation by the other equations x coefficient. (remember that to multiply an equation by a number is to multiply both sides of the equal sign by that number.)

so:
6 (5x-5) =6 (-7y)
30x - 30 = -42y

5 (6x+5y) = 5 (-11)
30x + 25y = -55

now I subtract the 2 equations.

I will subtract the left sides of equations and subtract the right sides of equations on other side

30x - 30 - (30x + 25y) = -42y - (-55)

distribute the minus sign into the parenthesis

30x - 30 - 30x - 25y = -42y + 55

cancel out the x values

- 30 - 25y = -42y + 55

solve for t
17y = 85
Y = 5

plug y into either equation
6x + 5(5) = -11
6x + 25 = -11
6x = - 36
x = -6

answer (5,-6)

this can be checked by plugging the values into other equatiin

Answer 2

hmm
add 7y+5 to both sides of 1st equation
5x+7y=5
eliminate x's
multiply first equation by -6 and 2nd by 5 and add them

-30x-42y=-30
30x+25y=-55 +
0x-17y=-85

-17y=-85
divide both sides by -17
y=5
sub back
5x-5=-7y
5x-5=-7(5)
5x-5=-35
add 5
5x=-30
divide 5
x=-6

x=-6
y=5
subsitute to find out

5x-5=-7y
5(-6)-5=-7(5)
-30-5=-35
-35=-35
yep

6x+5y=-11
6(-6)+5(5)=-11
-36+25=-11
-11=-11
yep


x=-6
y=5
(-6,5)