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Problem 324

# Solve $$x+y=3$$ $$2 x+3 y=1$$

Expert verified
The solution to the system of equations is $$x=8$$ and $$y=-5$$.
See the step by step solution

## Step 1: Solve one equation for one variable

We will start by solving the first equation for y: $$x+y=3$$ Subtract x from both sides of the equation to isolate y: $$y=3-x$$

## Step 2: Substitute the expression for y into the other equation

Now we will substitute the expression $$3-x$$ for y in the second equation: $$2x + 3y = 1$$ Replace y with its expression: $$2x + 3(3-x) = 1$$

## Step 3: Solve for x

Now, we need to solve this equation for x. First, distribute the 3 to the terms inside the parentheses: $$2x + 9 - 3x = 1$$ Now, combine like terms: $$2x - 3x + 9 = 1$$ Solve for x: $$-x = -8$$ $$x = 8$$

## Step 4: Find the value of y

Now that we have the value of x, we can find the value of y by substituting the value of x into the expression we found for y in step 1: $$y = 3 - x$$ $$y = 3 - 8$$ $$y = -5$$

## Step 5: Write the solution

Our solution is: $$x = 8$$ and $$y = -5$$ So, the system of equations is solved by the values $$x=8$$ and $$y=-5$$.

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