In the following exercises, determine if the following...

In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
x+y=2 \\
y=\frac{3}{4} x
\end{array}\right.
$$
(a) $\left(\frac{8}{7}, \frac{6}{7}\right)$
(b) $\left(1, \frac{3}{4}\right)$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. Such systems are investigated to find common solutions that satisfy all the equations simultaneously, often representing the intersection of lines or planes in a geometric context.

Solution to a System of Equations

A solution to a system of equations is a set of values for the variables that, when substituted into each equation, result in true statements. The solution represents the point or set of points where the graphs of the equations intersect, confirming that all conditions imposed by the equations are met.

Substitution Method

The substitution method involves replacing the variable in one equation with its equivalent expression from another equation to verify if a particular set of variable values satisfies the entire system. This method is used to test candidate solutions, ensuring that each equation holds true when the candidate values are applied.

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