How do you solve y = 3x - 4 and 2x - y = 1?

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Answer 1 · 2015-09-25T04:33:37

The solution is $(x, y) = (3, 5)$ $(x,y)=(3,5)$

Hence you have two linear equations we have that

$y = 3 x - 4$ $y=3x-4$ and $y = 2 x - 1$ $y=2x-1$

since the first parts are equal so the second are

$3 x - 4 = 2 x - 1 \Rightarrow x = 3$ $3x-4=2x-1=>x=3$ and $y = 2 \cdot 3 - 1 = 5$ $y=2*3-1=5$

Answer 2 · 2015-09-25T04:38:52

$x = 3$ $x = 3$
$y = 5$ $y = 5$

$y = 3 x - 4$ $y= 3x - 4$ $\Rightarrow$ $rArr$ 1st equation
$2 x - y = 1$ $2x - y = 1$ $\Rightarrow$ $rArr$ 2nd equation

Since $y$ $y$ is already the subject of the first equation, all you need to do is substitute $y = 3 x - 4$ $y = 3x - 4$ into the 2nd equation!

So,

$2 x - (3 x - 4) = 1$ $2x - (3x - 4) = 1$

Expand the brackets.

$2 x - 3 x + 4 = 1$ $2x - 3x + 4 = 1$

Which gets you:

$- x + 4 = 1$ $-x + 4 = 1$

Move the 4 over so $x$ $x$ becomes your subject.

$- x = - 4 + 1$ $-x = -4 + 1$
$- x = - 3$ $-x = -3$

Switch them over so your $x$ $x$ is positive!

$3 = x$ $3 = x$

To find $y$ $y$ , just substitute $x = 3$ $x = 3$ into either the 1st of 2nd equation.

So,

$y = 3 (3) - 4$ $y = 3(3) - 4$
$y = 9 - 4$ $y= 9 - 4$
$y = 5$ $y = 5$

To check:
Substitute the values of $x$ $x$ and $y$ $y$ back into the equation. You will get the same answer.