the sum of the digits of a two-digit number is 8. if the number is multiplied by 4 the result is 104 write and solve a system of equations find the number.
Let the digit in the 10th place be=T
Let the digit in the 1st. place be =F, then we have:
T + F=8, but,
4(10T + F)=104, so the two are:
26
Solve the following system:
{4 (F+10 T) = 104 | (equation 1)
F+T = 8 | (equation 2)
Express the system in standard form:
{4 F+40 T = 104 | (equation 1)
F+T = 8 | (equation 2)
Subtract 1/4 × (equation 1) from equation 2:
{4 F+40 T = 104 | (equation 1)
0 F-9 T = -18 | (equation 2)
Divide equation 1 by 4:
{F+10 T = 26 | (equation 1)
0 F-9 T = -18 | (equation 2)
Divide equation 2 by -9:
{F+10 T = 26 | (equation 1)
0 F+T = 2 | (equation 2)
Subtract 10 × (equation 2) from equation 1:
{F+0 T = 6 | (equation 1)
0 F+T = 2 | (equation 2)
Collect results:
Answer: | T=2 and F=6
