# How do you solve by substitution x+y=2 and 3x+2y=5?

$x = 1$ & $y = 1$

#### Explanation:

Given equations

$x + y = 2 \setminus \ldots \ldots . . \left(1\right)$

$3 x + 2 y = 5 \setminus \ldots \ldots . . \left(2\right)$

Substituting $y = 2 - x$ from (1) in (2) as follows

$3 x + 2 \left(2 - x\right) = 5$

$3 x + 4 - 2 x = 5$

$x + 4 = 5$

$x = 1$

substituting $x = 1$ in (1), we get

$1 + y = 2$

$y = 1$

Jul 23, 2018

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#### Explanation:

If $x + y = 2$
$x = 2 - y$

Put this into the second equation:

$3 \times \left(2 - y\right) + 2 y = 5$

$6 - 3 y + 2 y = 5$

$6 - 5 = y$

$y = 1$

Since $x + y = 2$

$x = 2 - y = 2 - 1 = 1$

$x = 1$ and $y = 1$
Or $x = y = 1$