Question

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

Answer 1

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:

$\begin{gathered} \Rightarrow4a+12=10 \\ \Rightarrow4a=10-12 \\ \Rightarrow4a=-2 \\ \Rightarrow a=-\frac{2}{4} \\ \Rightarrow a=-\frac{1}{2} \end{gathered}$

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.