solve by subsitution
2x+3y=10
x+6y=32
from the second : x = 32-6y
plug into the first
2(32-6y) + 3y = 10
expand, simplify and solve for y
then sub that y value into x = 32 - 6y
To solve the system of equations using substitution, we will solve one equation for one variable and substitute the expression into the other equation.
Let's solve the second equation for x:
x + 6y = 32
Subtract 6y from both sides:
x = 32 - 6y
Now substitute this expression for x in the first equation:
2x + 3y = 10
Substitute 32 - 6y for x:
2(32 - 6y) + 3y = 10
Expand and simplify:
64 - 12y + 3y = 10
Combine like terms:
-9y + 64 = 10
Subtract 64 from both sides:
-9y = 10 - 64
Simplify:
-9y = -54
Divide both sides by -9:
y = (-54) / (-9)
y = 6
Now that we have the value of y, we can substitute it back into the second equation to find x:
x + 6y = 32
x + 6(6) = 32
x + 36 = 32
Subtract 36 from both sides:
x = 32 - 36
x = -4
Therefore, the solution to the system of equations is x = -4 and y = 6.