Mathematics
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:)

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(2) Answers
shafanisa

1) 3x-2y=14 y=5x So we plug in y=5x into 3x-2y=14 We get: 3x-2(5x)=14 3x -10x=14 -7x=14 x=-2 So we found x, now we need to find y. We can simply plug in x into the equation and get y. y=5x y=5(-2) y=-10 So your answer will be (-2,-10). 2)  x-2y= -2 y= 2x+4 Once again plug in y=2x+4 into x-2y=-2 x-2(2x+4) = -2 x-4x-8=-2 -3x-8=-2 -3x = 6 x= -2 Now we plug back in x and solve for y :) y=2x+4 y=2(-2)+4 y=-4+4 y=0 So our solution would be (-2,0). 3) x+2y=-7 x-5y=7 Multiply the second equation by -1 -x+5y=-7 Now add that equation with the other one:    x+2y=-7 +    -x+5y=-7 ----------------- 7y=-14 y=-2 Now plug in y=-2 and solve for x x+2y=-7 x+2(-2)=-7 x+(-4)=-7 x-4=-7 x=-3 So your solution would be (-3,-2).

trav1ty

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

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