Question - Solving a System of Linear Equations using Substitution Method
Solution:
To solve the question provided in the image, we'll follow the steps shown:1. We substitute the value of $$ y $$ into the second equation $$ 2x = 9 $$, with the given $$ y = 5 - \frac{x}{2} $$.2. Now, we substitute $$ y $$ in the equation: \[ 2x = 9 \] $$ 2x = (5 - \frac{x}{2}) $$3. Next, we distribute the negative sign across the equation: \[ 2x = 5 - \frac{x}{2} \]4. To combine like terms, we need to have all the $$ x $$ terms on one side with the same denominator. To do this, first, we can multiply every term by $$ 2 $$ to eliminate the fraction: \[ 2(2x) = 2(5) - 2(\frac{x}{2}) \] \[ 4x = 10 - x \]5. Add $$ x $$ to both sides to combine like terms: \[ 4x + x = 10 \] \[ 5x = 10 \]6. Finally, divide both sides by $$ 5 $$ to solve for $$ x $$: \[ \frac{5x}{5} = \frac{10}{5} \] \[ x = 2 \]Now that we have the value of $$ x $$, we can substitute it back into the original equation $$ y = 5 - \frac{x}{2} $$ to find the value of $$ y $$:\[ y = 5 - \frac{2}{2} \]\[ y = 5 - 1 \]\[ y = 4 \]So the solution to the system of equations is $$ x = 2 $$ and $$ y = 4 $$.
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