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Where the lines intersect that gives the values for x and y in the two equations. The lines should intersect at (1, -3) because x = 1 and y = -3
-2
Those two statements are linear equations, not lines. If the equations are graphed, each one produces a straight line. The lines intersect at the point (-1, -2).
They intersect at points (-2/3, 19/9) and (3/2, 5) Solved by combining the two equations together to equal nought and then using the quadratic equation formula to find the values of x and substituting these values into the equations to find the values of y.
Compare the equations. If it has the same slope it most likely will be parallel which means it has 0 solutions. However, if you plug in points and they match up exactly it would have an infinite amount of solutions. The only way it would intersect more than once or 2 then would be if it was a parabola which would have a x^2 value typically. If it has 1 solution it means it would intersect once.
Sometimes. Not always.
first get both your equations into standard form... x + 2y = 9 (equation 1) x + 2y = 13 (equation 2) multiply equation 1 by (-1) -x - 2y = -9 x + 2y = 13 add the equations together 0 + 0 = 4 0 = 4 since the equations dont equal out then these equations do not intersect and are therefore parallel. PARALLEL is your answer
Where the lines intersect that gives the values for x and y in the two equations. The lines should intersect at (1, -3) because x = 1 and y = -3
-2
If it is a linear system, then it could have either 1 solution, no solutions, or infinite solutions. To understand this, think of two lines (consider a plane which is just 2 dimensional - this represents 2 variables and 2 equations, but the idea can be extended to more dimensions).If the 2 lines intersect at a point, then that point represents a solution. If the lines are parallel, then they never intersect, and there is no solution. If the equations are such that they are just different ways of describing the same line, then they intersect at every point, so there are infinite solutions. If you have more than 2 lines then maybe some of them will intersect, but this is not a solution for the whole system. If all lines intersect at a single point, then that is the single solution for the whole system.If you have equations that describe something other than a straight line, then it's possible that they may intersect in more than one point.
2
Those two statements are linear equations, not lines. If the equations are graphed, each one produces a straight line. The lines intersect at the point (-1, -2).
y = x - 1 y - x = 3 y = x - 1 y = x + 3 Since both equations represent straight lines that have equal slopes, 1, then the lines are parallel to each other. That is that the lines do not intersect, and the system of the equations does not have a solution.
They intersect at points (-2/3, 19/9) and (3/2, 5) Solved by combining the two equations together to equal nought and then using the quadratic equation formula to find the values of x and substituting these values into the equations to find the values of y.
-18 X + Y = 8 ........ 1 -3 X - Y = -2 ........ 2 Summing eq 1 and 2 - 21 X = 6 or X = - 6/21 or -2/7 Multiply eq 2 by 6 and subtract 2 from 1 7 Y = 20 or Y = 20/7 Accordingly, the two equations intersect at point: X = -2/7 and Y = 20/7
they intersect at point (1,-2)
None. If you rearrange each equation into slope intercept form ( y = mx + b), see below, you'll find that both equations have the same slope. Therefore they are parallel which also means would not intersect. Since the lines wouldn't intersect there is no solution to the system of equations.x + 3y = 23y = -x + 2y = (-1/3)x + 2/32x + 6y = -36y = -2x - 3y = (-1/3)x - (1/2)