# SOLUTION: 1: Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result. 2: Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result. 3: Determin

Algebra ->  Algebra  -> Graphs -> SOLUTION: 1: Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result. 2: Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result. 3: Determin      Log On

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 Question 68733: 1: Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result. 2: Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result. 3: Determine graphically the vertices of the triangle, the equation of whose sides are given y=x; y=0; 2x+3y=10, interpret the result?Answer by rmromero(383)   (Show Source): You can put this solution on YOUR website!1: Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result. To graph the equations, rewrite the equations written in standard form to slope-intercept form of the equation. y = mx + b 2x-3y=6 3y = 2x + 6 y = 2/3x + 2 2x+y=-10 y = -2x - 10 To solve for the intercept, We will use substitution method. 1. In either equation, solve for one variable in terms of the other. 2x+y=-10 y = -2x - 10 2. Substitute for that variable in the other equation. Solve. 2x-3y=6 2x - 3(-2x-10) = 6 2x + 6x + 30 = 6 8x + 30 = 6 8x = -24 x = -3 3. Substitute the result from step 2 in either equation. Solve for the other variable. 2x+y=-10 , x = -3 2(-3)+y = -10 -6 + y = -10 y = -4 4. Check the solution in both original equations. 2x+y=-10, x = -3, y = -4 2(-3) + (-4) = -10 -6 -4 = -10 -10 = -10 --------->> True 2x-3y=6, x = -3, y = -4 2(-3)-3(-4) = 6 -6 + 12 = 6 6 = 6 ---------->> True Therefore the lines intersect when x = -3 and y = -4 2: Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result. To graph the equations, rewrite the equations written in standard form to slope-intercept form of the equation. y = mx + b 2x+4y=10 4y = -2x+10 y = (-2/4)x+10/4 y = (-1/2)x+(5/2) 3x+6y=12 6y = -3x+12 y = (-3/6)x+(12/6) y = (-1/2)x+2 To solve for the intercept, We will use substitution method. 1. In either equation, solve for one variable in terms of the other. 3x+6y=12 6y = -3x+12 y = (-3/6)x+(12/6) y = (-1/2)x+2 2. Substitute for that variable in the other equation. Solve. 2x+4y=10 2x + 4((-1/2)x+2) = 10 2x + -2x + 8 = 10 8 = 10 ---------->> Not True Therefore the lines do not have an intersection. 3: Determine graphically the vertices of the triangle, the equation of whose sides are given y=x; y=0; 2x+3y=10, interpret the result? Graph each equation y=0. Since y=x, then x=0. To graph 2x+3y =10, we are going find y-intercept and x-intercept 2x+3y=10 To find y-intercept by substituting 0 for x. 2(0) + 3y = 10 3y = 10 y = 10/3 ----->y-intercept (0, 10/3) To find x-intercept by substituting 0 for y. 2x + 3(0) = 10 2x = 10 x = 5 --------->> x-intercept (5, 0) Notice that the y-intercept (0, 10/3) is one of the vertex of the triangle. x-intercept (5, 0) is the other vertex of the triangle formed. And lastly, the origin (0,0).