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:

Using cross-method:

(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!