{:[12 t=4v-3],[-6t=4v+6]:} If (t,v) is the solution to the system of equations, what is the value of t-v ? ◻

Question

{:[12 t=4v-3],[-6t=4v+6]:} If  (t,v) is the solution to the system of equations, what is the value of  t-v ?  ◻

Bytelearn · Accepted Answer

Write Equations: First, let's write down the system of equations we need to solve: 1) 12t = 4v - 3 2) -6t = 4v + 6 We need to find the values of t and v that satisfy both equations simultaneously.Elimination Method: To solve the system, we can use the method of elimination or substitution. Let's use elimination by adding the two equations together to eliminate v. Before we do that, we need to make the coefficients of v the same in both equations. We can multiply the second equation by -1 to get the coefficients of v to be opposites. Multiplying the second equation by -1 gives us: -1 * (-6t) = -1 * (4v + 6) 6t = -4v - 6 Now we have: 1) 12t = 4v - 3 3) 6t = -4v - 6Add Equations: Next, we add equations 1) and 3) together to eliminate v: (12t) + (6t) = (4v - 3) + (-4v - 6) This simplifies to: 18t = -9Solve for t: Now we can solve for t by dividing both sides of the equation by 18: 18t / 18 = -9 / 18 t = -1/2Substitute for v: With the value of t found, we can substitute it back into one of the original equations to find v. Let's use equation 1): 12t = 4v - 3 12(-1/2) = 4v - 3 -6 = 4v - 3Add 3 to Solve for v: Now, we add 3 to both sides of the equation to solve for v: -6 + 3 = 4v - 3 + 3 -3 = 4vDivide by 4 for v: Finally, we divide both sides by 4 to find the value of v: -3 / 4 = 4v / 4 v = -3/4Find t - v: Now that we have both t and v, we can find the value of t - v: t - v = (-1/2) - (-3/4) To subtract these fractions, we need a common denominator, which is 4: t - v = (-2/4) - (-3/4) t - v = (-2/4) + (3/4) t - v = 1/4

$\begin{array}{r} 12 t=4 v-3 \\ -6 t=4 v+6 \end{array}$ $\newline$ If $(t, v)$ is the solution to the system of equations, what is the value of $t-v$ ? $\newline$ $\square$

Full solution

More problems from Write an equation word problem

Related topics

12t=4v−3−6t=4v+6 \begin{array}{r} 12 t=4 v-3 \\ -6 t=4 v+6 \end{array} 12t=4v−3−6t=4v+6​\newlineIf (t,v) (t, v) (t,v) is the solution to the system of equations, what is the value of t−v t-v t−v ?\newline□ \square □

$\begin{array}{r} 12 t=4 v-3 \\ -6 t=4 v+6 \end{array}$ $\newline$ If $(t, v)$ is the solution to the system of equations, what is the value of $t-v$ ? $\newline$ $\square$