Question

How do you solve x+2y=5 and 2x-3y=-4?

Answer 1

If P is the point where the two graphs cross then;

`color(purple)(=> P_("crossing point") = (x,y)->(0.7,1.8) ->(7/10,9/5)`

Explanation:

Given:
`color(brown)(x+2y=5)`................................(1)
`color(brown)(2x-3y=-4)`........................(2)

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Using short cut methods: (jumping steps)

`color(blue)("Making y the dependant variable:")`
`y=-x+5/2....................(1_a)`
`y=2/3x+4/3......................(2_a)`

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`color(blue)("To determine the value of "x)`

By substitution we can equate equation `(1_a)` to equation `(2_a)` through `y` giving:

`-x+5/2=y=2/3x+4/3`

Collecting like terms

`2/3x+x=5/2-4/3`

`5/3x= (15-8)/6`

`color(blue)(x=7/6xx3/5=7/10)`...........................(3)
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`color(blue)("To determine the value of "y)`

Substitute equation (3) into equation `(1_a)`. The easier of the two!

`y=-7/10+5/2`

`y= (25-7)/10`

`y=18/10 = 9/5`

`color(blue)(y=9/5)`

Note: `y=9/5 = 1.8" and "x=7/10=0.7`

`=> P_("crossing point") = (x,y)->(0.7,1.8)`