hayrea99
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# SOLVE BY SUBSTITUTION: 3x-2y=14 y=5x solve by substitution x-2y=-2 y=2x+4 solve by elimination x+2y=-7 x-5y=7 PLEASE HELP WORTH 10 POINTS! AKA SHOW WORK:)

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)