At what point do two lines with the equations 7x-3y=13 and y=2x-3 intersect?
920287
Use substitution.\n\n7x - 3y = 13\n\n7x - 3(2x-3) = 13\n\n7x - 6x + 9 = 13\n\nx + 9 = 13\n\nx = 4\n\nThen go back and plug in to find y\n\ny = 2x - 3\n\ny = 2(4) - 3\n\ny = 8 - 3\n\ny = 5\n\n(4,5) is the answer.
852759
3x+7y=3\n7y=-3x+3\ny=-3/7*x+3/7\nSlope=-3/7\nWe have the slope and point[-6,7]\nWe will find the intercept\n7=-3/7*-6+c\nc=7-18/7\n=[49-18]/7\n=31/7\nWe now have the slope and intercept\nThe equation is\ny=-3/7*x+31/7\n7y+3x-31=0
811970
ok so parallel lines mean they have the same slopes so u know \n-13=(y-15)/(4-3)\n  remember slope is rise/run or the change in y / change in x\n\nso -13 =y-15  y=-13+15 or   y=2
969004
1) Simply add the two equations.  This will cancel the y's\n3x = 13\nDivide both sides by 3\nx = 13/3\nReplace x with 13/3 in one of the equations to find y\nx + y = 4, so\n13/3 + y = 4\ny = 4 - 13/3\ny = 12/3 - 13/3 = -1/3\nAnswer: x = 13/3 and y = -1/3\n\n2) Use substitution.  Replace y with (5/4)x in the first equation\n-10x + 8y = -6 becomes\n-10x + 8(5/4)x = -6\nSimplify\n-10x + 10x = -6\n0 = -6\nSince this is false, there is no solution.\n\n3) Multiply the first equation by -2 and add this to the second equation.\n-2x + 4y = -8\n2x - y = 4\n3y = -4\ny = -4/3\nReplace y with -4/3 in one of the equations and solve for x.\n2x - y = 4\n2x - (-4/3) = 4\n2x + 4/3 = 4\n2x = 4 - 4/3\n2x = 12/3 - 4/3\n2x = 8/3\nDivide both sides by 2\nx = 4/3\nAnswer: x = 4/3 and y = -4/3
282740
y=Mx+b\nSubstitute for y and x with given poiunts:\n\n1 = m(-13) + b\n\nSubstitute for m\n\n1 = 4(-13) + b\n\nSolve\n\n1 = -52 + b\n\n53 = b
701694
7x + y = 1 (subtract 7x from both sides)\ny = 1 - 7x\n\n3x + 2y = -9 (substitute in for y)\n3x + 2(1 - 7x) = -9\n3x + 2 - 14x = -9 (subtract 2 from both sides)\n-11x = -11\nx = 1\n\ny = 1 - 7x (substitute in for x)\ny = 1 - 7(1)\ny = 1 - 7\ny = -6\n\nAnswer: (1, -6)
565039
For this you are asked to take the the equation y = 2n + 3 and substitute the rest of the values in for n and solve the equation. The implied operation between 2 and n is multiplication.\n\nSo you take the n out of the equation and put in the values that you have listed.\n\nFirst Value:\ny = 2(2) + 3  Do the multiplication first then add the 3\ny = 4 + 3\ny = 7\n\nSecond Value:\ny = 2(1/2) + 3\ny = 1 + 3\ny = 4\n\nThird Value:\ny = 2(0) + 3\ny = 3
819556
Hey, here's the setup for these types of problems.\nYou want the equation in the form of y = mx + b\nsince we know that x = 2, y = -7, and m = -1/5, we can plug these values into that equation to find the equation of the line that passes through the desired point. SO:\n-7 = (-1/5)(2) + b\n-7 = (-2/5) + b\nb = (-7)+(2/5)\nb = -33/5\nso the equation for the line is:\ny = (-1/5)x - (33/5)\n\nhope that helps!!
872809
If the equation is lineear, or a line like it sounds like, the equation is y=mx+b. m is the slope or ten. and b is the y-int. or -130, and you are done
813958
We can use the point-slope form of the equation and then transform it into the slope-intercept form.\n\n(y - y1) = m(x - x1)\n(y - 2) = 4/3(x - 3)\ny - 2 = (4/3)x - 4\ny  =(4/3)x - 2.\n\nm = 4/3, b = -2\n\n3y = x - 3\ny = (1/3)x - 1\n\nThe slope m = 1/3
638546
6-2y=7y+13\nor,-2y-7y=13-6\nor,-9y=9\nor,y=-1
964525
Y = mx + b\nWhere  m is the slope of the line ond\nb is the y intercept
724639
2x-4y = 3.8\n3x - y = 17.7\n\nmultiply second equation by -4 so that when u add them both u will cancel the y's...\n2x-4y = 3.8\n-12x+4y = -70.8\n\nnow add them..\n\n-10x = -67\n     x = 67/10 = 6.7\n\nnow plug this x in for any one of the original equations and solve for y....\n\n2(6.7) - 4y = 3.8\n\n13.4 - 4y = 3.8\n-4y = -9.6\n   y = -9.6/-4 = 2.4\n\nso the solution is (6.7,2.4)
1073694
If you're given that:\n\nP1 is at (x1,y1) \nP2 is at (x2,y2)\n\nand you're looking for: \n\nP3 at (x3,y3)\n\nIf the length of the line from P1 to P3 is L1\nand the length of the line from P2 to P3 is L2\n\nThen you can solve for the single point which\nsatisfies both of:\n\nL1 = SQRT( (X3-X1)**2 + (Y3-Y1)**2 )\nL2 = SQRT( (X3-X2)**2 + (Y3-Y2)**2 )\n\nTo simplify the math, square both sides of each eq:\n\nL1**2 = (X3-X1)**2 + (Y3-Y1)**2 \nL2**2 = (X3-X2)**2 + (Y3-Y2)**2\n\nSince you're given the first two points and\nthe lengths to the last point, the terms\nX1, Y1, X2, Y2, and L1, L2 are all constants. \nOnce you plug in the constant values, you're\nleft with two equations and just two unknowns \n(X3 and Y3).\n\nSolve for X3 and Y3 using a little algebra.
187414
2^y = 64/y\n\n\nthis is the intersection of two curves:\nt=2^y\nand\nt=64/y\n\nthat is an exponential and an equilateral hyperbola.\nPlotting the graphs you can have an idea of the intersection (in this case you have the exact solution by plotting integer values, but in general you may need to solve by iterative numeric formulas, after finding graphically a rough estimate of the solution)
245713
More completely, given two lines ax1 + bx2 = c and dx1 + ex2 = f, they can either intersect completely, in which case the solution set is a line, or they can intersect in one point, or they can not intersect at all (parallel lines). This is due to Euclidean geometry.\nIf you're more of an algebraist, suppose they intersected at more than one point (x1, x2) and (y1, y2). Then ax1 + bx2 = ay1 + by2 and dx1 + ex2 = dy1 + ey2. But then (a-d)x1 + (b-e)x2 = (a-d)y1 + (b-e)y2, so (d-a)/(b-e) = (y2-x2)/(y1-x1). Suppose we chose another point (z1, z2) on the line formed by (y1, y2) and (x1, x2). But note that (z1, z2) will also satisfy the equations, hence the entire line satisfies the equations whenever more than one point satisfies the equation. This is just the first case given above (the lines completely overlap). \nNote the degenerate condition (x1,x2)=(y1,y2) of a single solution gives an undefined quotient 0/0.
375327
Where x = 0, the line intercepts the y-axis:\n\n1. 5x-2y =10 \n2y = 5x - 10\ny = (5/2)x - 5 \ny-int = (0, -5)\n\n2. 2y+7x =14\n2y = -7x + 14\ny = (-7/2)x + 7\ny-int = (0, 7)\n\n3. x=3\nHas no y-intercept\n\n4. 1/2x-2y=8\n2y = (1/2)x - 8\ny = (1/4)x - 4\ny-int = (0, -4)