Question

7. If (2,- 1) is the solution to the following linear system, what are the values of a and b?

Answer 1

Answer:

• Considering ax + by = -7

${ \tt{ax + by = - 7}} \\ \\ { \tt{(a \times 2) + (b \times - 1) = - 7}} \\ \\ { \boxed{ \tt{2a - b = - 7 \: - - - eqn \{1 \}}}}$

• make b the subject of eqn{1}

${ \tt{b = 2a + 7 - - - eqn \{2 \}}}$

• considering 2ax - 3by = 1

${ \tt{2ax - 3by = 1}} \\ \\ { \tt{(2a \times 2) - (3b \times - 1) = 1}} \\ \\ { \boxed{ \tt{4a + 3b = 1 - - - eqn \{3 \}}}}$

• substitute b in eqn{3} with b from eqn{2}

${ \tt{4a + 3(2a + 7) = 1}} \\ \\ { \tt{4a + 6a + 21 = 1}} \\ \\ { \tt{10a = - 20}} \\ \\ { \boxed{ \boxed{ \tt{ \: \: a = - 2 \: \: }}}}$

• find b using eqn{2}

${ \tt{b = 2a + 7}} \\ \\ { \tt{b = (2 \times - 2) + 7}} \\ \\ { \tt{b = - 4 + 7}} \\ \\ { \boxed{ \boxed{ \tt{ \: \: b = 3 \: \: }}}}$