For each system find the values of a and b so that the solution set to the system is (5,12)

step 1 In this problem, we're told that the ordered pair 512 is a solution to the given system of equat

For each system find the values of a and b so that the...

Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations sharing the same variables. The solution to such a system is the set of values for the variables that simultaneously satisfy all equations. When the system is composed of two lines in the coordinate plane, solving the system involves finding the point(s) where the lines intersect.

Slope-Intercept Form

The slope-intercept form of a line is written as y = mx + c, where m represents the slope and c is the y-intercept. This form makes it easy to understand a line’s direction and where it crosses the y-axis, and it is useful for analyzing how different parameters affect the graph of the line.

Unique Intersection Point

When two lines intersect at exactly one point, the coordinates of this intersection represent the unique solution to the system. Ensuring that a line passes through a specific point means that its equation must satisfy the coordinate values of that point, which is critical when determining unknown parameters in the equation.

Substitution Method for Parameter Determination

The substitution method involves plugging the known coordinates of the unique solution into each linear equation to solve for any unknown parameters. This technique allows one to tailor the equation’s parameters so that the line will pass through the designated point.

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