Question

solve the system of equations.
y=6x+35
y=9x+14
x =
y =

Explanation:

Step1: Set equations equal (substitution)

Since $y = 6x + 35$ and $y = 9x + 14$, set them equal:
$$6x + 35 = 9x + 14$$

Step2: Isolate x terms

Subtract $6x$ from both sides:
$$35 = 3x + 14$$

Step3: Isolate constant terms

Subtract 14 from both sides:
$$21 = 3x$$

Step4: Solve for x

Divide both sides by 3:
$$x = \frac{21}{3} = 7$$

Step5: Substitute x to find y

Plug $x=7$ into $y=6x+35$:
$$y = 6(7) + 35 = 42 + 35 = 77$$

Answer:

$x = 7$
$y = 77$