How do you solve 2x+3y=31 and y=x+7?

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Answer 1 · 2018-04-26T00:40:30

$x = 2$ $x=2$ and $y = 9$ $y=9$

We have:

$2 x + 3 y = 31$ $2x+3y=31$ ..... [A]
$y=x+7 \ \ \ \ \ \ \$ ..... [B]

We can perform a direct substitution of Eq [B] into Eq [A] giving:

$2x+3(x+7)=31$

Now, we collect terms and solve for $x$ :

$2x+3(x)+(3)7=31$

$:. 2x+3x+21=31$
$:. 2x+3x=31 -21$
$:. 5x=10$
$:. x=2$

Now we can substitute $x$ into [B] and solve for $y$

$y = 2+7$
$:. y=9$

And having gained the solution $x=2$ and $y=9$ , we can validate the result using Eq [A]:

$2x + 3y = (2)(2) + (3)(9) = 4 + 27 = 31$ , as expected.