How do you solve the system of equations by using substitution: y = x + 5 and y = 2x - 7?

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How do you solve the system of equations by using substitution: y = x + 5 and y = 2x - 7?

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Answer 1 · 2016-05-18T12:15:26

Solve the first equation for x, substitute into the second equation, and get the answer of $x = 12$ $x=12$ and $y = 17$ $y=17$

Explanation:

To solve using substitution, we'll take one of the equations (the first one - it's a very simple one), solve for x, and then substitute it into the second one.

So let's first take $y = x + 5$ $y=x+5$ and solve for $x$ $x$ :

$y = x + 5$ $y=x+5$ - subtract 5 from both sides and we get

$y - 5 = x$ $y-5=x$

And now we can substitute that into the 2nd equation:

$y = 2 x - 7$ $y=2x-7$
$y = 2 (y - 5) - 7$ $y=2(y-5)-7$

and let's simplify

$y = 2 y - 10 - 7$ $y=2y-10-7$ - we can subtract $2 y$ $2y$ from both sides and combine terms
$- y = - 17$ $-y=-17$
$y = 17$ $y=17$

We can now substitute the y value back into the given equations and find the x value:

$y = x + 5$ $y=x+5$
$17 = x + 5$ $17=x+5$
$x = 12$ $x=12$

$y = 2 x - 7$ $y=2x-7$
$17 = 2 x - 7$ $17=2x-7$
$24 = 2 x$ $24=2x$
$x = 12$ $x=12$

And we're done! $x = 12$ $x=12$ and $y = 17$ $y=17$

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How do you solve the system of equations by using substitution: y = x + 5 and y = 2x - 7?

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