Solve the simultaneous equations using graph method (x + y=2).(x _y=4) make y the subject of the formula for number a x+y=2

Mathematics

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Answers

2 parts
1

x=3,y=−1x=3, y=-1

2

2 - x

Step-by-step solution

6 steps

Let's break this down into two parts.

Part 1· 4 steps

Solve the simultaneous equations using the graph method

The given equations are:

  1. x+y=2x + y = 2
  2. x−y=4x - y = 4
  1. Find two points for the first equation, x+y=2x + y = 2.

    • If x=0x = 0, then y=2y = 2. Point: (0,2)(0, 2).
    • If y=0y = 0, then x=2x = 2. Point: (2,0)(2, 0). These points define the first line.
  2. Find two points for the second equation, x−y=4x - y = 4.

    • If x=0x = 0, then −y=4  ⟹  y=−4-y = 4 \implies y = -4. Point: (0,−4)(0, -4).
    • If y=0y = 0, then x=4x = 4. Point: (4,0)(4, 0). These points define the second line.
  3. Identify the intersection point.

    When these two lines are plotted on a graph, their intersection point is the solution. From the graph, the lines intersect at (3,−1)(3, -1).

  4. Verify the solution.

    Substitute x=3x=3 and y=−1y=-1 into both original equations:

    • For x+y=2x + y = 2: 3+(−1)=2  ⟹  2=23 + (-1) = 2 \implies 2 = 2 (True)
    • For x−y=4x - y = 4: 3−(−1)=4  ⟹  3+1=4  ⟹  4=43 - (-1) = 4 \implies 3 + 1 = 4 \implies 4 = 4 (True) Both equations are satisfied.

    The solution to the simultaneous equations is:

    x=3x = 3 y=−1y = -1

    The solution is x=3,y=−1\boxed{x=3, y=-1}.

Part 22 - x

Make yy the subject of the formula for x+y=2x+y=2

  1. Start with the given equation.

    x+y=2x + y = 2
  2. Subtract xx from both sides of the equation to isolate yy.

    y=2−xy = 2 - x

    So, yy as the subject of the formula is:

    y=2−xy = \boxed{2 - x}
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