Question

please help: Use the substitution method to solve the linear system.
-x+3y=4
x+6y=14
different problem
3x+2y=8
x+4y=-4

Answer 1

Choose one equation from each pair and solve for y. Then substitute that y into the second equation.
IE
3x+y=4
x+2y=7

Solving for y the first equation becomes y=-3x+4.
Plug that in for y in the second equation:
x+2(-3x+4)=7
Simplify for x.
-5x=1
x=-1/5

choose one of original equations and plug in x and solve for y.
3(-1/5)+y=4
y=23/5

Answer 2

-x+3y=4
x+6y=14

Take an equation: x + 6y = 14
Then make it equal x.

x + 6y = 14
- 6y -6y

x = - 6y + 14

Then plug x into the first equation that was not used:
-(- 6y + 14) + 3y = 4
6y - 14 + 3y = 4
9y - 14 = 4
+14 +14

9y = 18
/9 /9

y = 2

Then plug y into either equation
-x+3y=4
-x + 3(2) = 4
-x + 6 = 4
-6 -6

-x = -2
/-1 /-1

x = 2

The solution for the first problem is x = 2 and y = 2