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Explain Bot To find the values of x and y that satisfy the given system of equations, we can use a method called substitution.
Step 1: Solve the first equation for x in terms of y.
2x - 6y = 28
2x = 6y + 28
x = (6y + 28)/2
x = 3y + 14
Step 2: Substitute the expression for x in the second equation.
ax + by = 14
a(3y + 14) + by = 14
3ay + 14a + by = 14
Step 3: Rearrange the equation to isolate the variable y.
3ay + by = 14 - 14a
y(3a + b) = 14 - 14a
y = (14 - 14a) / (3a + b)
Step 4: Substitute the expression for y back into the equation for x.
x = 3y + 14
x = 3((14 - 14a) / (3a + b)) + 14
Simplify as needed to find the expression for x.
By solving for y in terms of a and b, and then substituting it back into the equation for x, we can find the values of x and y that satisfy the system of equations.