1.5 a-4.5 b=3(a+b) 5.5 b=5(b-a)+2.5 a If (a,b) is the solution to the system of equations, then what is the value of b-a ?

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1.5 a-4.5 b=3(a+b)  5.5 b=5(b-a)+2.5 a If  (a,b) is the solution to the system of equations, then what is the value of  b-a ?

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Write Equations: Write down the given system of equations. The system of equations is: 1.5a - 4.5b = 3(a + b) 5.5b = 5(b-a) + 2.5aSimplify First Equation: Simplify the first equation. Distribute the 3 on the right side of the first equation: 1.5a - 4.5b = 3a + 3b Now, move all terms involving variables to one side to set the equation to zero: 1.5a - 4.5b - 3a - 3b = 0 Combine like terms: -1.5a - 7.5b = 0Simplify Second Equation: Simplify the second equation. Distribute the 5 on the right side of the second equation: 5.5b = 5b - 5a + 2.5a Combine like terms: 5.5b = 5b - 2.5a Now, move all terms involving variables to one side to set the equation to zero: 5.5b - 5b + 2.5a = 0 Combine like terms: 0.5b + 2.5a = 0Solve System of Equations: Solve the simplified system of equations. We now have the system: -1.5a - 7.5b = 0 2.5a + 0.5b = 0 Multiply the second equation by 15 to make the coefficient of b the same in both equations: 15(2.5a + 0.5b) = 15(0) 37.5a + 7.5b = 0Eliminate b: Add the two equations together to eliminate b. -1.5a - 7.5b = 0 37.5a + 7.5b = 0 ----------------- 36a = 0 Divide both sides by 36 to solve for a: a = 0/36 a = 0Find a: Substitute the value of a into one of the original simplified equations to find b. Using the second simplified equation: 2.5a + 0.5b = 0 Substitute a = 0: 2.5(0) + 0.5b = 0 0 + 0.5b = 0 Divide both sides by 0.5 to solve for b: b = 0/0.5 b = 0Find b: Calculate b - a. Since both a and b are 0: b - a = 0 - 0 b - a = 0

$\begin{aligned} 1.5 a-4.5 b & =3(a+b) \\ 5.5 b & =5(b-a)+2.5 a \end{aligned}$ $\newline$ If $(a, b)$ is the solution to the system of equations, then what is the value of $b-a$ ?

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1.5a−4.5bamp;=3(a+b)5.5bamp;=5(b−a)+2.5a \begin{aligned} 1.5 a-4.5 b &amp; =3(a+b) \\ 5.5 b &amp; =5(b-a)+2.5 a \end{aligned} 1.5a−4.5b5.5b​amp;=3(a+b)amp;=5(b−a)+2.5a​\newlineIf (a,b) (a, b) (a,b) is the solution to the system of equations, then what is the value of b−a b-a b−a ?

$\begin{aligned} 1.5 a-4.5 b & =3(a+b) \\ 5.5 b & =5(b-a)+2.5 a \end{aligned}$ $\newline$ If $(a, b)$ is the solution to the system of equations, then what is the value of $b-a$ ?