standard_description: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
problem_activity: Problem 1
Graph the system of equations in the coordinate plane and identify the solution.
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Problem 2
Graph the system of equations in the coordinate plane. Identify the solution to the system and verify it algebraically.
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Problem 3
Line
$$a$$
is shown on the coordinate grid. Construct line
$$b$$
on the coordinate grid so that
Line
$$a$$
and line
$$b$$
represent a system of linear equations with a solution of (
$$6$$
,
$$-2$$
).
The slope of line
$$b$$
is greater than
$$-1$$
and less than
$$0$$
.
The
$$y$$
-intercept of line
$$b$$
is positive.
[IMG]


aligns: no