How do you solve $2 x + 3 y = 12$ $2x + 3y = 12$ and $x + 4 y = 11$ $x + 4y = 11$ ?

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Answer 1 · 2018-05-28T01:13:28

$x = 3, y = 2$ $x=3, y=2$

Let's start with the second equation and solve for $x$ $x$ in terms of $y$ $y$ .

We can subtract $4 y$ $4y$ from both sides to get

$x = 11 - 4 y$ $color(blue)(x=11-4y)$

We have solved for $x$ $x$ in terms of $y$ $y$ , so we can plug this into the first equation. We get

$2 (11 - 4 y) + 3 y = 12$ $2(11-4y)+3y=12$

Distributing the $2$ $2$ , we get

$22 - 8 y + 3 y = 12$ $22-8y+3y=12$

Combining like terms, we get

$22 - 5 y = 12$ $22-5y=12$

We can subtract $22$ $22$ from both sides to get

$- 5 y = - 10$ $-5y=-10$

Dividing both sides by $- 5$ $-5$ , we get

$y = 2$ $y=2$

To completely solve for $x$ $x$ , we can go back to the equation I have in blue, and plug in $y = 2$ $y=2$ . We get

$x = 11 - 4 (2)$ $x=11-4(2)$

$x = 11 - 8$ $x=11-8$

$x = 3$ $x=3$

Thus, $x = 3$ $x=3$ and $y = 2$ $y=2$ .

Hope this helps!

How do you solve 2x+3y=122x + 3y = 12 and x+4y=11x + 4y = 11?