Question

Decide whether the ordered pair is a solution of the system. $$\begin{aligned}&2 x+4 y=2\\\&-x+5 y=13 \quad(-3,2)\end{aligned}$$

Short answer

Yes, the ordered pair (-3,2) is a solution to the given system of equations.

Step-by-step solution

Substitute Values in the First Equation

Insert the values from the ordered pair (-3,2) into the first equation, resulting in the equation \(2(-3)+4(2)=2\). This simplifies to -6+8, which equals 2.

Substitute Values in the Second Equation

Then, we substitute the values from the ordered pair (-3,2) into the second equation, resulting in the equation \(-(-3)+5(2)=13\). This simplifies to 3+10, which equates to 13.

Conclusion of the Verification

Since the ordered pair (-3,2) satisfies both equations, it can be concluded that it is indeed a solution to the system of equations.