How do you solve $2 x + y = 7$ $2x + y = 7$ and $4 x - y = 23$ $4x - y = 23$ ?

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Answer 1 · 2016-03-06T09:42:15

$x, y = 5, - 3$ $x,y=5,-3$

$1) 2 x + y = 7$ $color(blue)(1) )color(blue)(2x+y=7$

$2) 4 x - y = 23$ $color(blue)(2))color(blue)(4x-y=23$

We can eliminate $y$ $y$ from the first equation by $- y$ $-y$ in the second equation

Add both of the equations

$\to (2 x + y = 7) + (4 x - y = 23)$ $rarr(2x+y=7)+(4x-y=23)$

$\to 6 x = 30$ $rarr6x=30$

$\Rightarrow x = \frac{30}{6} = 5$ $color(green)(rArrx=30/6=5$

Now substitute the value of $x$ $x$ to the first equation

$\to 2 (5) + y = 7$ $rarr2(5)+y=7$

$\to 10 + y = 7$ $rarr10+y=7$

$\Rightarrow y = 7 - 10 = - 3$ $color(green)(rArry=7-10=-3$

How do you solve 2x+y=72x + y = 7 and 4x−y=234x - y = 23 ?