Questions: Solve the following system of linear equations by graphing: -5/3 x + 1/2 y = 7/5 -20/3 x + 2 y = 1

Transcript text: Solve the following system of linear equations by graphing: \[ \begin{array}{r} -\frac{5}{3} x+\frac{1}{2} y=\frac{7}{5} \\ -\frac{20}{3} x+2 y=1 \end{array} \]

Solution

Solution Steps

Step 1: Convert the first equation to slope-intercept form

Given the equation: \[ -\frac{5}{3} x + \frac{1}{2} y = \frac{7}{5} \] First, isolate $ y $: \[ \frac{1}{2} y = \frac{5}{3} x + \frac{7}{5} \] Multiply both sides by 2: \[ y = \frac{10}{3} x + \frac{14}{5} \]

Step 2: Convert the second equation to slope-intercept form

Given the equation: \[ -\frac{20}{3} x + 2 y = 1 \] First, isolate $ y $: \[ 2 y = \frac{20}{3} x + 1 \] Divide both sides by 2: \[ y = \frac{10}{3} x + \frac{1}{2} \]

Final Answer

The equations in slope-intercept form are: \[ y = \frac{10}{3} x + \frac{14}{5} \] \[ y = \frac{10}{3} x + \frac{1}{2} \]

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (10/3)x + (14/5)", "y = (10/3)x + (1/2)"], "latex_expressions": ["$y = \\frac{10}{3}x + \\frac{14}{5}$", "$y = \\frac{10}{3}x + \\frac{1}{2}$"]}

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