# Question:Solution exists, but solve fails

## Question:Solution exists, but solve fails

Maple

Maple 15.

I have a set of equations I can solve manually, but, solve fails.

restart;
eq1 := tgtX[1] = 0;
eq2 := tgtY[2] - y[2]    = m[2]*(tgtX[2]-x[2]);
eq3 := tgtY[3] - y[3]    = m[3]*(tgtX[3]-x[3]);
eq4 := tgtY[4] - y[4]    = m[4]*(tgtX[4]-x[4]);
eq5 := tgtY[2] - tgtY[1] = vy*t[2];
eq6 := tgtY[3] - tgtY[1] = vy*t[3];
eq7 := tgtY[4] - tgtY[1] = vy*t[4];
eq8 := tgtX[2]           = vx*t[2];
eq9 := tgtX[3]           = vx*t[3];
eq10:= tgtX[4]           = vx*t[4];
#
# solve the equations
eqs  := {eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10};

solvx := solve(eq10,vx);
solvy := solve(eq7,vy);
sol1  := subs(vx=solvx,{eq8,eq9});
sol2  := subs(vy=solvy,{eq5,eq6});

soln  := subs(sol1,{eq2,eq3});

soln  := subs(tgtY[2]=solve(sol2[1],tgtY[2]),soln);
soln  := subs(tgtY[3]=solve(sol2[2],tgtY[3]),soln);
soln  := subs(tgtY[1]=solve(soln[1],tgtY[1]),soln[2]);
soln  := solve({eq4,soln},{tgtX[4],tgtY[4]});

# this returns empty solution
solve(eqs,{tgtX[4],tgtY[4]});

Any ideas?

Tom Dean

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