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The y intercept is -1

Q: What is the point of intersection for y equals 2x -1?

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1,6

3x + y + 1 = 0y = - 3x - 12x - 3y + 8 = 03y - 2x - 8 = 03y = 2x + 8y = 2x/3 + 8/3-3x - 1 = 2x/3 + 8/3-9x - 3 = 2x + 8-11x = 11x = -1y = -3x - 1 = 3 - 1 = 2The graphs intersect at the point (-1, 2).

If: y = x^2 +2x +2 and y = 7 -2x Then: x^2 +2x +2 = 7 -2x Transposing terms: x^2 +4x -5 = 0 Factorizing the above: (x +5)(x -1) = 0 meaning x = -5 or x = 1 By substitution into original equations points of intersection are at: (-5, 17) and (1, 5)

Perpendicular equation: x+2y = 0 Point of intersection: (2, -1) Perpendicular distance: square root of 5

2

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They intersect when 2x + 4 = -x + 1 or 3x = -3 => x = -1 and when x = -1, y = -x + 1 = -(-1) + 1 = 2 So the point of intersection is (-1, 2)

1,6

2X-Y=3 X+Y=3 ---------- 3X = 6 X=2 2(2)-Y=3 4-Y=3 Y=1 Point of interesection: (2,1).

3x + y + 1 = 0y = - 3x - 12x - 3y + 8 = 03y - 2x - 8 = 03y = 2x + 8y = 2x/3 + 8/3-3x - 1 = 2x/3 + 8/3-9x - 3 = 2x + 8-11x = 11x = -1y = -3x - 1 = 3 - 1 = 2The graphs intersect at the point (-1, 2).

The point of intersection is when a set value of x and y works in both equations - this is a set of simultaneous equations to solve:4y - 2x = 75y - 3x = 65×(1) - 4×(2) → (20y - 20y) + (-10x - -12x) = 35 - 24 → 2x = 11solving (3) gives x = 5.5Substituting for y in (2) gives 5y - 3 × 5.5 = 6 → 5y = 22.5 → y = 4.5Checking by substituting for y and x in (1) gives 4×4.5 - 2×5.5 = 18 - 11 = 7 as required→ the point of intersection of 4y - 2x = 7 and 5y - 3x = 6 is (5.5, 4.5)

If: y = x^2 +2x +2 and y = 7 -2x Then: x^2 +2x +2 = 7 -2x Transposing terms: x^2 +4x -5 = 0 Factorizing the above: (x +5)(x -1) = 0 meaning x = -5 or x = 1 By substitution into original equations points of intersection are at: (-5, 17) and (1, 5)

2

Perpendicular equation: x+2y = 0 Point of intersection: (2, -1) Perpendicular distance: square root of 5

x2-x3+2x = 0 x(-x2+x+2) = 0 x(-x+2)(x+1) = 0 Points of intersection are: (0, 2), (2,10) and (-1, 1)

The point (4, 5) is.

y = 5y = -2x + 3Since both of those things are equal to 'y', they're equal to each other.5 = -2x + 3Add 2x to each side:5 + 2x = 3Subtract 5 from each side:2x = -2Divide each side by 2:x = -1The point of intersection is (-1, 5) .

It works out that the points of intersection between the equations of 2x+5 = 5 and x^2 -y^2 = 3 are at: (14/3, -13/3) and (2, 1)