systems of linear equations

[Deb Sturm]

1. 0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3

0.2x(10)+0.4y(10)=1.7(10)
2x+4y=17

8.3x(10)-6.3y(10)=-4.3(10)
83x=63y=-43

63(2x+4y=17)
4(83x-63y=-43)

126x+252y=1071
332x-252y=-172

458x=899
x=899/458 (1.96)

126(899/458) + 252y = 1071
56637/229 + 252y = 1071

252y=188622/229

y=1497/458 (3.27) (and x=899/458 (1.96))
I am confused on how to graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection. Is this when I do ordered pairs? I've confused myself badly. Thanks for any help! Deb

 

[srmichael]

1. 0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3

0.2x(10)+0.4y(10)=1.7(10)
2x+4y=17

8.3x(10)-6.3y(10)=-4.3(10)
83x=63y=-43

63(2x+4y=17)
4(83x-63y=-43)

126x+252y=1071
332x-252y=-172

458x=899
x=899/458 (1.96)

126(899/458) + 252y = 1071
56637/229 + 252y = 1071

252y=188622/229

y=1497/458 (3.27) (and x=899/458 (1.96))
I am confused on how to graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection. Is this when I do ordered pairs? I've confused myself badly. Thanks for any help! Deb

Do you know how to find the x and y intercepts when given a line in the form Ax + BY = C? The point of intersection [note that there is only one point of intersection, not points, unless the two lines are either parallel (no points of intersection) or the same line (infinite points of intersection)] is the point you just solved for in the system of equations. If you graph these two lines using the x and y intercepts, they should intersect at that point (1.96, 3.27).