Question

solve the system of equations graphed on the coordinate axes below.
$y = \frac{3}{4}x + 1$
$y = -\frac{4}{3}x + 1$

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( \frac{3}{4}x + 1 = -\frac{4}{3}x + 1 \)

Step2: Subtract 1 from both sides

Subtracting 1 from both sides gives: \( \frac{3}{4}x = -\frac{4}{3}x \)

Step3: Add \( \frac{4}{3}x \) to both sides

Adding \( \frac{4}{3}x \) to both sides: \( \frac{3}{4}x + \frac{4}{3}x = 0 \)
Find a common denominator (12) and combine the fractions: \( \frac{9}{12}x + \frac{16}{12}x = 0 \) which simplifies to \( \frac{25}{12}x = 0 \)

Step4: Solve for \( x \)

Multiply both sides by \( \frac{12}{25} \): \( x = 0 \)

Step5: Substitute \( x = 0 \) into one of the original equations

Using \( y = \frac{3}{4}x + 1 \), substitute \( x = 0 \): \( y = \frac{3}{4}(0) + 1 = 1 \)

Answer:

The solution to the system is \( (0, 1) \)