Question

solve the following linear system by elimination: 4x + 3y = 12 and 4x - y = 4

Answer 1

Answer:

4x + 3y=12 and 4x - y =4

Step-by-step explanation:

subtracting both equations we get

4x-3y -4x +y = 12- 4

-2y = 8

y = -4

and

4x + 3×(-4) = 12

4x - 12 =12

4x = 24

x = 6

Answer 2

Step-by-step explanation:

$4x+3y=12 {\dots}{\dots}(1)$

$4x-y =4 {\dots}{\dots}(2)$

Now

• By multiplying -1 with eq (1) and 3 with eq (2) we get

$4x+3y=12 {\dots }{\dots}(3)$

$-12x+3y=-12 {\dots}{\dots }(4)$

$\:\:{(+)}\:\;{(-)}\:\: {(+)}$

_____________________________

By subtraction we get

${:}\longrightarrow$$16x=24$

${:}\longrightarrow$$x={\dfrac {24}{16}}$

${\therefore}$${\underline{\boxed{\bf {x={\dfrac {3}{2}}}}}}$

• Substitute the value of x in eq (2)

${:}\longrightarrow$$4 ({\dfrac {3}{2}})-y=4$

${:}\longrightarrow$${\dfrac {12}{2}}-y=4$

${:}\longrightarrow$$6-y=4$

${:}\longrightarrow$$-y=4-6$

${:}\longrightarrow$$-y=-2$

$\therefore$${\underline{\boxed{\bf {y=2}}}}$

$\therefore$Your answer is${\boxed {(x,y)=({\dfrac {3}{2}}\:,\:2)}}$