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Find the value of (a) that makes the ordered pair a solution to the equation.

Find the value of (a) that makes the ordered pair a solution to the equation.-example-1

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The first coordinate of the ordered pair is the x-value, while the second coordinate corresponds to the y-value.

Part a)


4x-3y=10

Substitute x=a and y=-4 to find an equation for a:


4(a)-3(-4)=10

Solve for a:


\begin{gathered} \Rightarrow4a+12=10 \\ \Rightarrow4a=10-12 \\ \Rightarrow4a=-2 \\ \Rightarrow a=-(2)/(4) \\ \Rightarrow a=-(1)/(2) \end{gathered}

Therefore, the value of a that makes the ordered pair (a,-4) a solution to the equation 4x-3y=10, is -1/2.

Part b)


y=-5x+2

Substitute x=3 and y=a+1:


a+1=-5(3)+2

Solve for a:


\begin{gathered} \Rightarrow a+1=-15+2 \\ \Rightarrow a+1=-13 \\ \Rightarrow a=-13-1 \\ \Rightarrow a=-14 \end{gathered}

Therefore, the value of a that makes the ordered pair (3,a+1) a solution to the equation y=-5x+2, is -14.

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