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Solve the following simultaneous equation

x+2y=1,3x-y=17

Solve the following simultaneous equation $\newline$ $x+2 y=1,3 x-y=17$

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Solve equations involving like terms

Full solution

Q. Solve the following simultaneous equation

\newline

x+2 y=1,3 x-y=17

Write Equations: Write down the given equations. $\newline$ We have two equations: $\newline$ $1$ ) $x + 2y = 1$ $\newline$ $2$ ) $3x - y = 17$
Solve for x: Solve one of the equations for one variable. $\newline$ Let's solve the first equation for $x$ : $\newline$ $x = 1 - 2y$
Substitute into Second Equation: Substitute the expression for $x$ into the second equation. $\newline$ Substitute $x = 1 - 2y$ into $3x - y = 17$ : $\newline$ $3(1 - 2y) - y = 17$
Combine Terms: Distribute and combine like terms. $\newline$ $3 - 6y - y = 17$ $\newline$ $-7y = 17 - 3$ $\newline$ $-7y = 14$
Solve for y: Solve for y. $\newline$ Divide both sides by $-7$ : $\newline$ $y = \frac{14}{-7}$ $\newline$ $y = -2$
Substitute for $x$ : Substitute the value of $y$ back into the expression for $x$ . $\newline$ Substitute $y = -2$ into $x = 1 - 2y$ : $\newline$ $x = 1 - 2(-2)$
Simplify for $x$ : Simplify the expression to find the value of $x$ . $x = 1 + 4$ $x = 5$

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