Answer:
a = -2 , b = -8
Step-by-step explanation:
* Lets talk about the solution of the linear equations
- There are three types of the solutions of the system of linear equations
# If the two lines intersect each other, then there is one solution
- The equations are ax+ by = c , dx + ey = f
# If the two lines parallel to each other, then there is no solution
- The equations are ax+ by = c , ax + by = d in its simplest form ,
where a is the coefficient of x , b is the coefficient of y and
c , d are the numerical terms
# If the two lines coincide (over each other), then there are infinite
solutions
- The equations are ax+ by = c , ax + by = c in its simplest form, where
a is the coefficient of x , b is the coefficient of y and c is the
numerical term
* Lets solve the problem
∵ The system of equation is:
ax - y = 8 ⇒ (1)
2x + y = b ⇒ (2)
∵ The system create infinitely many solutions
∴ The lines are coincide
- The equations must be equal, then multiply equation(1) or (2) by -1 to
make the coefficient of y in the two equations equal
∴ -ax + y = -8
∴ 2x + y = b
∵ Their coefficients of x are equal
∵ Their coefficients of y are equal
∵ Their numerical terms are equal
∵ The coefficient of x in equation (1) is -a and in equation (2) is 2
∴ -a = 2 ⇒ multiply both sides by -1
∴ a = 2
∵ The numerical term in equation (1) is -8 and in equation (2) is b
∴ b = -8
* The values for a and b will create infinitely many solutions are -2 , -8
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