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.