Question

use the substitution method to solve the system of equations. choose the correct ordered pair.
y = 5x - 17
y = x + 3
a. (4,7)
b. (5,8)
c. (1, -12)
d. (5, -17)

Explanation:

Step1: Substitute y from second equation

Since \( y = x + 3 \) and \( y = 5x - 17 \), substitute \( y \) in the first equation with \( x + 3 \). So we get \( x + 3 = 5x - 17 \).

Step2: Solve for x

Subtract \( x \) from both sides: \( 3 = 4x - 17 \). Then add 17 to both sides: \( 20 = 4x \). Divide both sides by 4: \( x = 5 \). Wait, no, wait, let's do it again. Wait, \( x + 3 = 5x - 17 \), subtract \( x \): \( 3 = 4x - 17 \), add 17: \( 20 = 4x \), so \( x = 5 \)? Wait, no, that's a mistake. Wait, let's check again. Wait, \( y = 5x -17 \) and \( y = x + 3 \), so set equal: \( 5x -17 = x + 3 \). Subtract \( x \): \( 4x -17 = 3 \). Add 17: \( 4x = 20 \), so \( x = 5 \)? But then \( y = 5 + 3 = 8 \), so (5,8)? But wait, let's check option A: (4,7). Let's test x=4: y=54 -17=20-17=3? No, wait, 54=20, 20-17=3, but y=x+3=7. Wait, that's a contradiction. Wait, I must have messed up. Wait, let's do it again. \( 5x -17 = x + 3 \). Subtract x: 4x -17 = 3. Add 17: 4x = 20. x=5. Then y=5+3=8. So (5,8) is option B. But wait, let's check option A: x=4, y=54 -17=3, but y=x+3=7. Not equal. Option B: x=5, y=55 -17=25-17=8, and y=5+3=8. So that works. Wait, but earlier I thought x=5, but let's check the equations again. Wait, the first equation is y=5x -17, second is y=x+3. So setting 5x -17 = x + 3. 5x -x = 3 +17. 4x=20. x=5. Then y=8. So (5,8) is correct, which is option B. Wait, but maybe I made a mistake earlier. Let's check option A: (4,7). For x=4, y=5*4 -17=20-17=3, but y=x+3=7. Not equal. So option B: (5,8) works. So the correct answer is B. (5,8)

Answer:

B. (5, 8)