Question

1)0 resolva as equações utilizando o método da substituição
a) {x + y = 10
{x - y = 4

b) {x - y = 15
{2x + y = 60

c) {x + 2y = 14
{y + 2x = 19

d) {2x - y = 15
{3y - x + 15

Answer 1

a) {x+y=10
{x-y=4
x=10-y
10-y-y=4
10-2y=4
-2y=4-10
-2y=-6.(-1)
2y=6
y=6/2
y=3
x=10-y
x=10-3
x=7
S={(7, 3)}
b) {x-y=15
{2x+y=60
x=15+y
2(15+y)+y=60
30+2y+y=60
2y+y=60-30
3y=30
y=30/3
y=10
x=15+y
x=15+10
x=25
S={(25, 10)}
c) {x+2y=14
{y+2x=19
x=14-2y
y+2.(14-2y)=19
y+28-4y=19
y-4y=19-28
-3y=-9.(-1)
3y=9
y=9/3
y=3
x=14-2y
x=14-2.3
x=14-6
x=8
S={(8, 3)}
d) {2x-y=15
{3y-x=15
-y=15-2x.(-1)
y=-15+2x
3y-x=15
3(-15+2x)-x=15
-45+6x-x=15
+6x-x=15+45
5x=60
x=60/5
x=12
y=-15+2x
y=-15+2.12
y=-15+24
y=9
S={(12, 9)}