Question

For what value of “m” will the pair of linear equations 2 + 3 = 7 and
have no solutions?

Answer 1

Answer:

2x+3y−7=0(m−1)x+(m+1)y=3m−1⟹y=7−2x3⟹y=3m−1−(m−1)xm+1

7−2x3(7−2x)(m+1)7m+7−2mx−2xmx−5xx(m−5)=3m−1−(m−1)xm+1=3(3m−1−(m−1)x)=9m−3−3mx+3x=2m−10=2(m−5)⟹x=2⟹m=5

Let’s move on with x=2.

y=7−2x3=7−2∗23=7−43=33=1

We now have a point at which both linear equations are the same. Let’s plug it in and solve for m.

y1m+1m+1m−3m+2m0=3m−1−(m−1)xm+1=3m−1−2(m−1)m+1=3m−1−2(m−1)=3m−1−2m+2=−1−1+2=0