Answer:
x = 4, y = 8
Step-by-step explanation:
If the triangles are congruent by the HL Theorem, it means that the hypotenuse and one leg of the right triangle are congruent to the corresponding one leg and hypotenuse of the other.
Thus;
2x - 5 = y - 5 (Eqn 1) and
y - 3 = x + 1 (Eqn 2)
Thus:
Rewrite equation 1
2x = y - 5 + 5
2x = y
Substitute y = 2x in equation 2.
y - 3 = x + 1 (Eqn 2)
2x - 3 = x + 1
Collect like terms
2x - x = 3 + 1
x = 4
Substitute x = 4 in equation 1
2x - 5 = y - 5 (eqn 1)
2(4) - 5 = y - 5
8 - 5 = y - 5
3 = y - 5
3 + 5 = y
8 = y
y = 8
From the graph, we can see that the graph crosses the x-axis at the point (1.5, 0) the graph also passes through point (1, 1) and the graph crosses the y-axis at the point (0, 3).
Therefore, points (1.5, 0), (1, 1) and (0, 3) are some of the solutions of the graph.
Answer:
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