The problem asks to solve the simultaneous equations $2 - 2y = x$ and $2y = 3x - 22$ using the given graph.

AlgebraSimultaneous EquationsLinear EquationsGraph InterpretationSolution Verification
2025/4/1

1. Problem Description

The problem asks to solve the simultaneous equations 22y=x2 - 2y = x and 2y=3x222y = 3x - 22 using the given graph.

2. Solution Steps

First, we observe the graph. The two lines intersect at a point. We can read the coordinates of this intersection point directly from the graph.
The intersection point appears to be approximately at (x,y)=(6,2)(x, y) = (6, -2).
Let's verify this solution algebraically.
We have the two equations:
22y=x2 - 2y = x (1)
2y=3x222y = 3x - 22 (2)
From (1), we can express xx in terms of yy:
x=22yx = 2 - 2y (3)
Substitute (3) into (2):
2y=3(22y)222y = 3(2 - 2y) - 22
2y=66y222y = 6 - 6y - 22
2y=166y2y = -16 - 6y
8y=168y = -16
y=2y = -2
Now, substitute y=2y = -2 into (3):
x=22(2)=2+4=6x = 2 - 2(-2) = 2 + 4 = 6
So, the solution is x=6x = 6 and y=2y = -2.

3. Final Answer

x = 6
y = -2

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