{:[-3a+5b=11],[6a+2b=26]:} Consider the given system of equations. If (a,b) is the solution to the system, then what is the value of (a)/(b) ?

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{:[-3a+5b=11],[6a+2b=26]:} Consider the given system of equations. If  (a,b) is the solution to the system, then what is the value of  (a)/(b) ?

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Multiply Equations: Let's solve the system of equations using the method of substitution or elimination. We will use the elimination method to eliminate one of the variables and solve for the other. First, we need to make the coefficients of one of the variables the same in both equations. We can multiply the first equation by 2 and the second equation by 3 to make the coefficients of 'a' the same.New System of Equations: After multiplying the first equation by 2, we get: 2(-3a + 5b) = 2(11) -6a + 10b = 22 And after multiplying the second equation by 3, we get: 3(6a + 2b) = 3(26) 18a + 6b = 78 Now we have the new system of equations: {:[-6a+10b=22],[18a+6b=78]:}Add Equations: Next, we add the two equations together to eliminate 'a': (-6a + 10b) + (18a + 6b) = 22 + 78 This simplifies to: -6a + 18a + 10b + 6b = 100 12a + 16b = 100Solve for 'a': Now we can solve for 'a' by isolating it on one side: 12a = 100 - 16b a = (100 - 16b) / 12Substitute 'a': We can substitute the expression for 'a' back into one of the original equations to solve for 'b'. Let's use the first original equation: -3a + 5b = 11 Substituting 'a', we get: -3((100 - 16b) / 12) + 5b = 11Simplify Equation: Now we simplify the equation: -3(100/12) + 3(16b/12) + 5b = 11 -25 + (4b) + 5b = 11 9b - 25 = 11Correct Mistake: We made a mistake in the previous step while distributing the -3 across the terms in the parentheses. Let's correct this and simplify again. -3((100 - 16b) / 12) + 5b = 11 -((300 - 48b) / 12) + 5b = 11 -25 + 4b + 5b = 11

$\begin{aligned} -3 a+5 b & =11 \\ 6 a+2 b & =26 \end{aligned}$ $\newline$ Consider the given system of equations. If $(a, b)$ is the solution to the system, then what is the value of $\frac{a}{b}$ ?

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−3a+5bamp;=116a+2bamp;=26 \begin{aligned} -3 a+5 b &amp; =11 \\ 6 a+2 b &amp; =26 \end{aligned} −3a+5b6a+2b​amp;=11amp;=26​\newlineConsider the given system of equations. If (a,b) (a, b) (a,b) is the solution to the system, then what is the value of ab \frac{a}{b} ba​ ?

$\begin{aligned} -3 a+5 b & =11 \\ 6 a+2 b & =26 \end{aligned}$ $\newline$ Consider the given system of equations. If $(a, b)$ is the solution to the system, then what is the value of $\frac{a}{b}$ ?