3x - 7y = 4 and -6x + y = 5

Answer 1

-6x+y=5

3x-7y=4

This can be solved by substitution. Take the first equation and solve for y

-6x+y=5 Add 6x to both sides

y=5+6x Substitute this into the second equation

3x-7(5+6x)=4 Not solve for x. Distribute the 7

3x-35-42x=4 Combine like terms

-39x-35=4 Add 35 to both sides

-39x=39 Divide both sides by -39

x=-1

Now solve for y.

y=5+6x

y=5+6(-1)

y=5-6

y=-1

(-1,-1) is the solution

Answer 2

3x-7y=4 double it

6x-14y=8

add

-6x+y=5

to get

-13y=13

y=-1

3x-7(-1)= 4

3x =4-7=-3

x=-3/3=-1

x=y=-1

another method is matrix algebra

another is graphing

graph the 2 lines the 2 equations represent and find their intersection point = (x,y) =(-1,-1)

do a sketch on graph paper, or use desmos or another online graphing calculator or a handheld graphing calculator likeTI83