# SOLUTION: 2. - Determine how many solutions exist - Use either elimination or substitution to find the solutions (if any) - Graph the two lines, labeling the x-intercepts, y-intercepts

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: 2. - Determine how many solutions exist - Use either elimination or substitution to find the solutions (if any) - Graph the two lines, labeling the x-intercepts, y-intercepts      Log On

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 Algebra: Linear Equations, Graphs, Slope Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Linear-equations Question 184719: 2. - Determine how many solutions exist - Use either elimination or substitution to find the solutions (if any) - Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection 0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3 need help desperately! Thank you. Answer by ankor@dixie-net.com(15660)   (Show Source): You can put this solution on YOUR website!- Determine how many solutions exist - Use either elimination or substitution to find the solutions (if any) Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection 0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3 : get rid of the decimals, multiply both equations by 10, results 2x + 4y = 17 83x - 63y = -43 ; We will use elimination; Multiply the 1st equation by 83 and the 2nd equation by 2: 166x + 332y = 1411 166x - 126y = -86 --------------------subtraction eliminates x, find y 458y = 1497 y = ; approx 3.3 on the graph Find x using eq: 2x + 4y = 17 2x + 4() = 17 2x + = 17 2x = - + 17 2x = - + 2x = x = * x = ; approx 2.0 on the graph : solution: x = ; y = ; this the point of intersection : Put both equations in the slope intercept form 2x + 4y = 17 4y = -2x + 17 y = x + y = x + Plot two points x = 4; y = 2 (substituted 4 for x in the above equation and found y) x = 0; y = ; (4.25) this is also the y intercept (when x=0) Graph of this calculate the x intercept (when y = 0) x + = 0 x = - Multiply both side by -2, results x = = 8 is the x intercept, confirmed on the graph : Do the same with the 2nd equation; 83x - 63y = -43 -63y = -83x - 43 63y = 83x + 43; multiplied by -1 y = x + Plot two points x = 0, y = ; approx .7 on the graph; this the y intercept x = 4, y = ; approx 6 on the graph : Add this to the above graph: : Calculate the x intercept of this equation: x + = 0 x = - Multiply both sides by 63 83x = 43 x = ; approx -.5 on the graph, (the x intercept Summarize Eq1: x intercept = 8.5, y intercept = 4.25 Eq2: x intercept = , y intercept = Point of intersection: x = ; y = (approx 2, 3.3 on the graph ; : This problems was very time consuming, please take time to study it and learn what's happening here. Carl