Question

solve the system of equations.
y = 8x + 15
y = x + 37
x =
y =

Explanation:

Step1: Set equations equal

Since \( y = 8x + 15 \) and \( y = x + 37 \), set \( 8x + 15 = x + 37 \).

Step2: Solve for x

Subtract \( x \) and 15: \( 8x - x = 37 - 15 \) → \( 7x = 22 \)? Wait, no, 37 - 15 is 22? Wait, 37 - 15 is 22? No, 37 - 15 is 22? Wait, 37 - 15: 37 - 10 is 27, 27 -5 is 22. Then \( 7x = 22 \)? Wait, no, 8x - x is 7x. Wait, maybe I miscalculated. Wait, 8x +15 = x +37. Subtract x: 7x +15 =37. Subtract 15: 7x=22? No, 37-15 is 22? Wait, 37-15: 37-10=27, 27-5=22. So 7x=22? Then x=22/7? Wait, no, that can't be. Wait, maybe the original equations are y=8x+15 and y=x+37. Let me check again. 8x +15 = x +37. Subtract x: 7x +15 =37. Subtract 15: 7x=22? Wait, 37-15 is 22. So 7x=22 → x=22/7≈3.14? But that seems odd. Wait, maybe I made a mistake. Wait, 37-15 is 22? Yes. 8x -x is 7x. So x=22/7. Then y = x +37 = 22/7 + 37 = 22/7 + 259/7 = 281/7≈40.14. But that seems strange. Wait, maybe the equations are y=8x+15 and y=x+37. Let me check with substitution. If x=22/7, then y=8*(22/7)+15=176/7 + 105/7=281/7, and y=x+37=22/7 +259/7=281/7. So that's correct. But maybe the problem was written with a typo? Wait, maybe it's y=8x+15 and y=x+37. So the solution is x=22/7, y=281/7. But that's a fraction. Alternatively, maybe the equations are y=8x+15 and y=x+37. So step by step:

1. Set 8x +15 = x +37 (since both equal y)
2. Subtract x from both sides: 7x +15 =37
3. Subtract 15 from both sides: 7x=22
4. Divide by 7: x=22/7
5. Then y = x +37 = 22/7 + 37 = 22/7 + 259/7 = 281/7

So the solution is x=22/7, y=281/7.

Answer:

\( x = \frac{22}{7} \), \( y = \frac{281}{7} \)