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x + 2y = 10
x = 10 – 2y — (1)
2y^2 – 7y + x = 0 — (2)
Sub (1) into (2):
2y^2 – 7y + (10 – 2y) = 0
2y^2 – 9y + 10 = 0
Solve for the quadratic equation in y:
(2y – 5)(y – 2) = 0
Using quadratic formula:
where a=2, b= -9, c=10
y = 5/2 or y = 2
Sub both values back into eqn. (1):
x = 5 or x = 6
Note that question requires you to input your answer as co-ordinates!
Final answer: (5, 5/2) and (6, 2)
By the way, when I was in Secondary School, my Maths teacher recommended this free website: https://www.geogebra.org/ which allows you to explore the shapes of different graphs and how the shape changes as you change some numbers around. It helped me to visualise better the graphs I was working with, and you can also use it to double-check your answers!