How do you solve $y = 2 x + 3$ and $y = 3 x + 1$ using substitution?

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Solution

Solving the given equation by using substitution method.
The substitution method involves getting the value of one variable from one equation in terms of another variable and putting this in the second equation to eliminate and find the value of another variable.
The given equations are,
$y = 2 x + 3 . . . . . . (1)$
$y = 3 x + 1 . . . . . . (2)$
Substitute equation $(1)$ in equation $(2)$ , we get
$\Rightarrow 2 x + 3 = 3 x + 1 \Rightarrow 2 x - 3 x = 1 - 3 \Rightarrow - x = - 2 ∴ x = 2$
Substitute the value of $x$ in equation $(1)$ , we get
$\Rightarrow y = 2 x + 3 \Rightarrow y = 2 (2) + 3 \Rightarrow y = 4 + 3 ∴ y = 7$
Hence, the value of $x = 2$ and $y = 7$ .

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