Question

Examine the system of equations.


y = 3/2x − 6,


y = −9/2x + 21


Use substitution to solve the system of equations. What is the value of y?

Answer 1

By substitution,

1.5x - 6 = -4.5x + 21

6x = 27

x = 4.5

Hence, y = 1.5(4.5) - 6 = 0.75

Answer 2

A system of equations can be solved by substitution method.

The value of y is 3/4

The system of equations is:

$\mathbf{y = \frac 32x - 6}$

$\mathbf{y = -\frac 92x + 21}$

Substitute $\mathbf{y = \frac 32x - 6}$ in $\mathbf{y = -\frac 92x + 21}$

$\mathbf{\frac 32x - 6 = -\frac 92x + 21}$

Collect like terms

$\mathbf{\frac 32x + \frac 92x= 6 + 21}$

$\mathbf{6x= 27}$

Divide both sides by 6

$\mathbf{x= \frac{27}{6}}$

$\mathbf{x= \frac{9}{2}}$

Substitute 9/2 for x in $\mathbf{y = -\frac 92x + 21}$

$\mathbf{y = -\frac 92 \times \frac 92 + 21}$

$\mathbf{y = -\frac{81}{4} + 21}$

Evaluate

$\mathbf{y = \frac{-81 + 84}{4}}$

$\mathbf{y = \frac{3}{4}}$

Hence, the value of y is 3/4

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