Class-10 cbse
Find whether the given pair of linear equations are consistent or not? If equations are consistent, find the solution graphically.
3x + 2y = 5
2x - 3y = 7
Answers
a1/a2=3/2
b1/b2=2/3
c1/c2=5/7
=> 3/2 is not equal to 2/3 and 5/7
So,
The following pair of linear equations is consistent
Step-by-step explanation:
ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:
24x2+25x−47=(−8x−3)(ax−2)−53
You should then multiply (−8x−3) and (ax−2) using FOIL.
24x2+25x−47=−8ax2−3ax+16x+6−53
Then, reduce on the right side of the equation
24x2+25x−47=−8ax2−3ax+16x−47
Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.
The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.