# How do you solve Y=2X-1 and Y=X+1?

Mar 27, 2016

$\left\{\begin{matrix}X = 2 \\ Y = 3\end{matrix}\right.$

#### Explanation:

Combining the two equations, we find:

$2 X - 1 = Y = X + 1$

Subtract $X$ from both ends to get:

$X - 1 = 1$

Add $1$ to both sides to get:

$X = 2$

Then:

$Y = X + 1 = 2 + 1 = 3$

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Notes

In general, given two equations in $X$ and $Y$, then you can (attempt to) solve by substitution as follows:

Choose one of the equations from which it is easiest to derive a formula for $X$ in terms of $Y$ or $Y$ in terms of $X$. Then substitute the resulting formula in the other equation to get an equation in one variable. Solve the resulting equation, then substitute the value you have found into one of the other equations to find the other variable's value.