Question

7 + 2y = 8x
3x - 2y = 0
Solve the system of equations by substitution

Answer 1

7+2y=8x
3x-2y=0
3x=2y
y=(3/2)x
7+2(3/2)(x)=8x
7+3x=8x
7=5x
x=7/5=1.4
y=(3/2)(7/5)
y=21/10=2.1

Answer 2

Answer: The required solution is (x, y) = (1.4, 2.1).

Step-by-step explanation: We are given to solve the following system of equations by the method of substitution :

`7+2y=8x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-2y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

From equation (ii), we have

`3x-2y=\\\\\Rightarrow 3x=2y\\\\\Rightarrow x=(2)/(3)y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of x from equation (iii) in equation (i), we get

`7+2y=8*(2)/(3)y\\\\\Rightarrow 21+6y=16y\\\\\Rightarrow 16y-6y=21\\\\\Rightarrow 10y=21\\\\\Rightarrow y=(21)/(10).\\\\\Rightarrow y=2.1`

From equation (iii), we get

`x=(2)/(3)*(21)/(10)=(7)/(5)=1.4.`

Thus, the required solution is (x, y) = (1.4, 2.1).