Question

ax + by = 6 -2x + 4y = 12 In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a + b ?

Answer 1

1

Explanation:

You want the value of the sum a+b if the line ax+by=6 graphs the same as the line -2x +4y = 12.

Dependent Equations

The equations describe the same line, so have infinite solutions, if the coefficients and constants are the same.

Here, we notice that the constant in the second equation (12) is double that in the first equation (6). We can make them the same by dividing the second equation by 2:

(-2x +4y)/2 = 12/2

-x +2y = 6

Since we want this to be the same line as ...

ax +by = 6

we must choose ...

• a = -1
• b = 2

Sum

Then the sum of the coefficients is ...

a + b = (-1) + (2) = 1

The value of a+b is 1.