Question

[100 PONTOS AJUDA PFV] Resolva os sistemas utilizando o método da substituição.
a) 2x + y= 1
5x + 3y = 7
b) m -
- 3n = 2
4m + 2n= -1
C) 3p+q=-2
2p - 5q=3
d) w + 2t =3
t= 1/4w

Answer 1

Resposta:

a)$\left \{ {{2x+y=1} \atop {5x+3y=7}} \right.$

$\left \{ {{y=1-2x} \atop {5x+3y=7}} \right.$

5x+3(1-2x)7

x=-4

y=1-2x(-4)

y=9

(x, y)= (-4, 9)

$\left \{ {{2x (-4) + 9=1} \atop {5x(-4) + 3 x 9=7}} \right.$

$\left \{ {{1=1} \atop {7=7}} \right.$

(x, y)=(-4 , 9)

(x, y)=(-4,9)

b)$\left \{ {{m- -3n=2} \atop {4m+2n=-1}} \right.$

$\left \{ {{m=2-3n} \atop {4m+2n=-1}} \right.$

4(2-3n)+2n=-1

n=$\frac{9}{10}$

m=2-3x $\frac{9}{10}$

m= -$\frac{7}{10}$

(m, n) = $( - \frac{7}{10}, \frac{9}{10})$

$\left \{ {{- \frac{7}{10} } -(-3) x \frac{9}{10} =2\atop } } }} \right.$

4x $(-\frac{7}{10}) +2x \frac{9}{10}=-1$

$\left \{ {{2=2} \atop {-1=-1}} \right.$

(m, n) $(-\frac{7}{10}, \frac{9}{10})$

(m,n)=$(-\frac{7}{10}, \frac{9}{10})$

C)$\left \{ {{3p+q=-2} \atop {2p-5q=3}} \right.$

$\left \{ {{q=-2-3p} \atop {2p-5(5q=3}} \right.$

2p-5(-2-3p)3

p= -$\frac{7}{17}$

q=-2-3x $(-\frac{7}{17})$

q=- $\frac{13}{17}$

(p, q) = $( - \frac{7}{17}, - \frac{13}{17})$

$\left \{ {{-2=-2} \atop {3=3}} \right.$

(p, q)= $(- \frac{7}{17}, - \frac{13}{17})$

d)$\left \{ {{w+2t=3} \atop {t=1 / 4w}} \right.$

w+2x $\frac{1}{4}$ w=3

w=2

t=$\frac{1}{4}$ x2

t=$\frac{1}{2}$

(t, w) = $(\frac{1}{2} , 2)$

$\left \{ {{3=3} \atop {\frac{1}{2}= \frac{1}{2}}} \right.$

(t, w) = $(\frac{1}{2},2)$

Explicação passo-a-passo: