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

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

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Answer 1 · 2016-01-21T17:16:08

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

$\Rightarrow P_{crossing point} = (x, y) \to (0.7, 1.8) \to (\frac{7}{10}, \frac{9}{5})$ $color(purple)(=> P_("crossing point") = (x,y)->(0.7,1.8) ->(7/10,9/5)$

Explanation:

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

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using short cut methods: (jumping steps)

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

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To determine the value of "x)$

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)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To determine the value of "y)$

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

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

$y= (25-7)/10$

$y=18/10 = 9/5$

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

Tony B

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

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

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

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