Question

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What is the x-coordinate of the point where the graphs of 8x + 2y = 5 and y=-3x +2 intersect?

Answer 1

`\boxed{ \text{ x = 0.5} }\\`

Explanation:

`\text{It sounds as if`

`\begin{array}{lll}(1) & 8x+ 2y =5 & \\(2) & y=-3x+2 & \\ & 2y=5-8x & \text{Subtracted 8x from each side}\\ & y = (5-8x )/( 2) & \text{Divided each side by 2}\\\end{array}\\\\`

`\text{Here are a few points for Equations (1) and (2).}\\\begin{array}rr\\x & y & x & y\\-1 & 6.5 & -1 & 5\\0 & 2.5 & 0 & 2\\1 & -1.5 & 1 & -1\\\end{array}\\\\`

`\text{Equation (1) is the red line in the graph below.}\\\text{Equation (2) is the blue line.}\\\text{The two lines cross at }{\textbf{x = 0.5}}\\\\\boxed{ \textbf{ x = 0.5} }\\\\`