Questions: Find the point of intersection of the lines in the figure, given that line A, in red, has equation y=x+3 and line B, in blue, has equation 2x+3y=10 x= help (fractions) y= help (fractions)

Find the point of intersection of the lines in the figure, given that line A, in red, has equation y=x+3 and line B, in blue, has equation 2x+3y=10 x= help (fractions) y= help (fractions)
Transcript text: Find the point of intersection of the lines in the figure, given that line $A$, in red, has equation $y=x+3$ and line $B$, in blue, has equation \[ \begin{array}{l} 2 x+3 y=10 \\ x=\square \text { help (fractions) } \\ y=\square \text { help (fractions) } \]
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Solution

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Solution Steps

Step 1: Substitute the first equation into the second equation

Given the equations y = x + 3 and 2x + 3y = 10, substitute the first equation into the second equation:

2x + 3(x + 3) = 10

Step 2: Solve for x

Simplify and solve for x:

2x + 3x + 9 = 10 5x = 1 x = 1/5

Step 3: Solve for y

Substitute the value of x back into either equation to solve for y. Using y = x + 3:

y = (1/5) + 3 y = 1/5 + 15/5 y = 16/5

Final Answer:

x = 1/5 y = 16/5

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