Explanation:
To solve the system of equations using substitution method, we will solve one equation for one variable and substitute the resulting expression into the other equation.
Let's solve the first equation, 2x + 10y = 14, for x:
2x + 10y = 14
Subtract 10y from both sides:
2x = 14 - 10y
Divide both sides by 2:
x = 7 - 5y/1
Now we will substitute this expression for x into the second equation, 5x - 9y = 1:
5x - 9y = 1
Substitute x = 7 - 5y:
5(7 - 5y) - 9y = 1
Distribute the 5:
35 - 25y - 9y = 1
Combine like terms:
35 - 34y = 1
Subtract 35 from both sides:
-34y = -34
Divide both sides by -34:
y = 1
Now that we have solved for y, we can substitute this value back into either equation to find x:
2x + 10y = 14
Substitute y = 1:
2x + 10(1) = 14
Simplify:
2x + 10 = 14
Subtract 10 from both sides:
2x = 4
Divide both sides by 2:
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 1.