Question

Find the values of p and q for which the system of the linear equation has

infinite number of solutions
2x -3y = 7
(p +q) x -(p+ q- 3) y =4p+q

unwanted ans will be reported

Answer 1

If it has infinite solutions

`\boxed{\sf (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)}`

`\\ \sf\longmapsto (2)/(p+q)=(3)/(p+q-3)`

`\\ \sf\longmapsto 2(p+q-3)=3(p+q)`

`\\ \sf\longmapsto 2p+2q-6=3p+3q`

`\\ \sf\longmapsto 2p-3p+2q-3q=6`

`\\ \sf\longmapsto -p-q=6`

`\\ \sf\longmapsto p+q=-6`

`\\ \sf\longmapsto p=-6-q`

Take p as 1

• .q=-6-1=-7