1)
\(3x-2y=14\\ \\ y=5x\)
We know y's value. Let's plug it in the equation.
\(y=5x\\ \\ 3x-2\cdot (5x)=14\\ \\ 3x-10x=14\\ \\ -7x=14\)
Divide both sides by -7.
\(x=-2\)
Now we have x's value. Let's plug it in the equation to find y.
\(x=-2\\ \\ y=5x\\ \\ y=5\cdot -2\\ \\ y=-10\)
Solution,
(-2, -10)
2)
\(x-2y=-2\\ \\ y=2x+4\)
Again we have y's value. Let's plug and solve.
\(y=2x+4\\ \\ x-2\cdot (2x+4)=-2\\ \\ x-(2\cdot 2x+2\cdot 4)=-2\\ \\ x-4x-8=-2\\ \\ -3x-8=-2\\ \\ -3x=-2+8\\ \\ -3x=6\\ \\ x=\frac { 6 }{ -3 } \\ \\ x=-2\)
Now we have x's value let's solve for y.
\(x=-2\\ \\ y=2x+4\\ \\ y=2\cdot (-2)+4\\ \\ y=-4+4\\ \\ y=0\)
Solution,
(-2, 0)
3)
\(x+2y=-7\\ \\ x-5y=7\)
Let's first multiply the first equation by -1
\(-1\cdot (x+2y)=-1\cdot -7\\ \\ -x-2y=7\)
Then let's add these new equation and the second equation.
\(-1\cdot (x+2y)=-1\cdot -7\\ \\ -x-2y=7\\ \\ x-5y=7\\ \\ (-x-2y)+(x-5y)=7+7\\ \\ -x+x-2y-5y=14\\ \\ -7y=14\\ \\ y=\frac { 14 }{ -7 } \\ \\ y=-2\)
Now we have y's value let's plug it and solve for x.
\(y=-2\\ \\ x+2y=-7\\ \\ x+2\cdot (-2)=-7\\ \\ x-4=-7\\ \\ x=-7+4\\ \\ x=-3\)
Solution,
(-3, -2)
