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

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

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Answer 1 · 2018-03-24T20:14:01

Using substitution, you can find the solution is $x = 1, y = 3$ $x=1, y=3$

Explanation:

The second expression $y = 2 x + 1$ $y=2x+1$ is already an expression ready to substitute! Since we know what $y$ $y$ is equivalent to, we can substitute it into the first expression:

$x + y = 4$ $x+y=4$

$x + (2 x + 1) = 4 \Rightarrow x + 2 x + 1 = 4$ $x+(2x+1)=4 rArr x+2x+1=4$

$x (1 + 2) + 1 = 4 \Rightarrow 3 x + 1 = 4$ $x(1+2)+1=4 rArr 3x+1=4$

$3xcancel(+1-1)=4-1 rArr 3x=3$

$color(red)(x=1)$

Now that we know what $x$ is equivalent to, we can solve for $y$

$y=2x+1 rArr y=2(1)+1=2+1$

$color(blue)(y=3)$

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

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