solve for x both elemination and substitution method 3x+7y=1 and 5x-4y-14=0
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Answers
Step-by-step explanation:
Answer:
x=2\frac{8}{47}x=2
47
8
y=-\frac{37}{47}y=−
47
37
Step-by-step explanation:
3x + 7y = 1 .............. eq(i)
5x - 4y - 14 = 0
=> 5x - 4y = 14 ........eq(ii)
Elimination Method:
Multiplying equation (i) by 4:
12x + 28y = 4 .........eq(iii)
Multiplying equation (i) by 7:
35x - 28y = 98 .......eq(iv)
Adding equation (iii) and equation (iv):
47x = 102
x=\frac{102}{47}x=
47
102
=2\frac{8}{47}=2
47
8
Putting value of x in equation (i):
7y =1 - \frac{306}{47}=1−
47
306
=-\frac{259}{47}=−
47
259
∴ y=-\frac{37}{47}y=−
47
37
Substitution Method:
From equation (i):
y=\frac{1-3x}{7}y=
7
1−3x
........... equation (v)
Putting value of y, from equation (v) into equation (ii):
5x-4.\frac{1-3x}{7} = 145x−4.
7
1−3x
=14
=> 35x - 4 + 12x = 14x7
=>47x = 98 + 4 = 102
∴ x = \frac{102}{47}
47
102
= 2\frac{8}{47}2
47
8
Putting value of x into equation (v):
y = \frac{1 - 3.\frac{102}{47} }{7} = - \frac{259}{329} = - \frac{37}{47}y=
7
1−3.
47
102
=−
329
259
=−
47
37
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