solve the following system of equations graphically on the set of axes below.

\y = 2x - 4\
\y = -x - 1\

plot two lines by clicking the graph.
click a line to delete it.

Question

solve the following system of equations graphically on the set of axes below.

\y = 2x - 4\
\y = -x - 1\

plot two lines by clicking the graph.
click a line to delete it.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Graphical Systems of Equations", "Linear Equations Graphing" ], "new_concepts": [], "current_concepts": [ "Graphical Systems of Equations", "Linear Equations Graphing" ] } ## Graph the first linear equation Using the *Linear Equations Graphing* knowledge point $$ \begin{aligned} &y = 2x - 4\ &\text{y-intercept: } (0, -4)\ &\text{Slope } m = 2 \implies \text{second point: } (1, -2) \end{aligned} $$ ## Graph the second linear equation Using the *Linear Equations Graphing* knowledge point $$ \begin{aligned} &y = -x - 1\ &\text{y-intercept: } (0, -1)\ &\text{Slope } m = -1 \implies \text{second point: } (1, -2) \end{aligned} $$ ## Find the intersection point Using the *Graphical Systems of Equations* knowledge point $$ \begin{aligned} &2x - 4 = -x - 1\ &3x = 3 \implies x = 1\ &y = -1 - 1 = -2\ &\text{Intersection: } (1, -2) \end{aligned} $$ The solution to the system of equations is $(1, -2)$. { "elements": [ { "type": "functiongraph", "params": [{"js": "2*x - 4", "latex": "y = 2x - 4"}, -10, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "y = 2x - 4", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-x - 1", "latex": "y = -x - 1"}, -10, 10], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "y = -x - 1", "withLabel": true } }, { "type": "point", "params": [[1, -2]], "properties": { "name": "(1, -2)", "size": 4, "color": "#5583F2", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Graphical Systems of Equations" ] }

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Question

Explanation:

Graph the first linear equation

Graph the second linear equation

Find the intersection point

Answer: