1 of 8 0-day streak

Solve simultaneous equations by substitution

Question 1 of 8

No calculator

Find the pair of values that satisfies both equations

Equation 1:

b = -4\,a + 27

Equation 2:

-a - 4\,b = 12

Use substitution. Give exact integer or fraction answers where a value is requested

(a)1 mark

Make \(b\) the subject of Equation 1 and replace it in Equation 2. After making a variable the subject, which equation results from the substitution?

-4\,b - \left(\frac{b - 27}{-4}\right) = 12

-4\,a + 27 = -4\,a + 27

-a + 4\left(-4\,a + 27\right) = 12

-a - 4\left(-4\,a + 27\right) = 12

-a + 16\,a + 27 = 12

(b)1 mark

Use substitution to find \(a\). Give an exact integer

\(a\)

Format: Give an exact integer

Substitute your value for \(a\) into the subject equation and find \(b\). Give an exact integer

\(b\)

Format: Give an exact integer