Let a, b, c, and d be real numbers with a, c 6= 0. prove that the lines y = ax+b and y = cx + d have the same x-intercept if and only if ad = bc

Step-by-step explanation:

We have got the lines :

Both lines intercept the x-axis in the point :

In all point from x-axis the y-component is equal to 0.

We replace the I point in the lines equations:

From the first equation :

From the second equation :

Then

Finally :

y = ax + b and y = cx + d have the same x-intercept ⇔ad=bc

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!