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Problem 1

# Find the point of intersection of each pair of straight lines. $$\begin{array}{l} y=3 x+4 \\ y=-2 x+14 \end{array}$$

Expert verified
The point of intersection of the given pair of straight lines is $$(2, 10)$$.
See the step by step solution

## Step 1: Set the y's equal to each other

Since both equations are in the form y = mx + b, we can set the y's equal to each other to find the value of x: $$3x + 4 = -2x + 14$$

## Step 2: Solve for x

Now we need to solve this equation to find the value of x: Add $$2x$$ to both sides of the equation: $$3x + 2x + 4 = -2x + 2x + 14$$ Simplifying, we get: $$5x + 4 = 14$$ Subtract 4 from both sides of the equation: $$5x + 4 - 4 = 14 - 4$$ Simplifying, we get: $$5x = 10$$ Now, divide by 5: $$\frac{5x}{5} = \frac{10}{5}$$ Simplifying, we get: $$x = 2$$

## Step 3: Substitute x into one of the equations to find y

Now that we have the value of x, we can substitute it into one of the equations to find the value of y. Let's use the first equation: $$y = 3x + 4$$ Substitute x = 2: $$y = 3(2) + 4$$

## Step 4: Solve for y

Now we solve for y: $$y = 6 + 4$$ $$y = 10$$

## Step 5: Write the solution as a coordinate point

Now that we have the values of x and y, we can write the solution as a coordinate point: The point of intersection of the given pair of straight lines is $$(2, 10)$$.

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