solve the system of equations below by graphing:

$y = -\frac{1}{2}x + 3$

$y = 3x - 4$

the solution is: (

Question

solve the system of equations below by graphing:

$y = -\frac{1}{2}x + 3$

$y = 3x - 4$

the solution is: (

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Linear Equations", "Graphical Solution of Systems" ], "new_concepts": [], "current_concepts": [ "Linear Equations", "Graphical Solution of Systems" ] } ## Graph the first linear equation Using the *Linear Equations* knowledge point $$ \begin{aligned} &y = -\frac{1}{2}x + 3\ &\text{y-intercept: } (0, 3)\ &\text{Slope } m = -\frac{1}{2}\ &\text{Second point: } (2, 2) \end{aligned} $$ ## Graph the second linear equation Using the *Linear Equations* knowledge point $$ \begin{aligned} &y = 3x - 4\ &\text{y-intercept: } (0, -4)\ &\text{Slope } m = 3\ &\text{Second point: } (2, 2) \end{aligned} $$ ## Find the intersection point Using the *Graphical Solution of Systems* knowledge point $$ \begin{aligned} &-\frac{1}{2}x + 3 = 3x - 4\ &7 = \frac{7}{2}x \implies x = 2\ &y = 3(2) - 4 = 2\ &\text{Intersection point: } (2, 2) \end{aligned} $$ Solve the system of equations below by graphing: $y = -\frac{1}{2}x + 3$ $y = 3x - 4$ The solution is: (2, 2) { "elements": [ { "type": "functiongraph", "params": [ { "js": "-0.5*x + 3", "latex": "y = -\frac{1}{2}x + 3" }, -10, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "y = -1/2x + 3", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "3*x - 4", "latex": "y = 3x - 4" }, -10, 10 ], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "y = 3x - 4", "withLabel": true } }, { "type": "point", "params": [ [2, 2] ], "properties": { "name": "(2, 2)", "size": 4, "color": "#5583F2", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Graphical Solution of Systems" ] }

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QUESTION IMAGE

Question

Explanation:

Graph the first linear equation

Graph the second linear equation

Find the intersection point

Answer: