Question

Solve the following systems using determinant
(a) 2x +3y=4
4x +6y=4 ​

Answer 1

it has no solution

Explanation:

first of all if we want to know that how many solutions does it the system we can know easly

• if a1/a2=b1/b2=c1/c2 then the system has infinite solution
• if a1/a2=b1/b2≠c1/c2 the system has no solution
• if a1/a2≠b1/b2 the system has no solution

so in this system a1=2,a2=4,b1=3,b2=6,c1=4&c2=4

so 2/4_3/6_4/4=(to becomfortable to compare we have to find the denominators LCM.LCM(4,6)=12

6/12=6/12≠12/12.

so the system has no solution.

&you can also solve by this way

2x+3y=4 (multiply by ‒2 to be y=0)

4x+6y=4

‒4x‒6y=‒8

4x+6y=4

= 0+0=‒4(error)

so it has no solution

i think it is clear & i hope it helps you.