Question

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

Answer 1

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

$3x-2y=\\\\\Rightarrow 3x=2y\\\\\Rightarrow x=\dfrac{2}{3}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

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

$7+2y=8\times\dfrac{2}{3}y\\\\\Rightarrow 21+6y=16y\\\\\Rightarrow 16y-6y=21\\\\\Rightarrow 10y=21\\\\\Rightarrow y=\dfrac{21}{10}.\\\\\Rightarrow y=2.1$

From equation (iii), we get

$x=\dfrac{2}{3}\times\dfrac{21}{10}=\dfrac{7}{5}=1.4.$

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

Answer 2

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