Question

Y=4050x+2949 y=5165x+93 Solve using the elimination method and the substitution method.

Answer 1

Solve the following system using elimination:
{y = 4050 x + 2949 | (equation 1)
{y = 5165 x + 93 | (equation 2)

Express the system in standard form:
{-(4050 x) + y = 2949 | (equation 1)
{-(5165 x) + y = 93 | (equation 2)

Swap equation 1 with equation 2:
{-(5165 x) + y = 93 | (equation 1)
{-(4050 x) + y = 2949 | (equation 2)

Subtract 810/1033 × (equation 1) from equation 2:
{-(5165 x) + y = 93 | (equation 1)
{0 x+(223 y)/1033 = 2970987/1033 | (equation 2)

Multiply equation 2 by 1033:
{-(5165 x) + y = 93 | (equation 1)
{0 x+223 y = 2970987 | (equation 2)

Divide equation 2 by 223:
{-(5165 x) + y = 93 | (equation 1)
{0 x+y = 2970987/223 | (equation 2)

Subtract equation 2 from equation 1:
{-(5165 x)+0 y = (-2950248)/223 | (equation 1)
{0 x+y = 2970987/223 | (equation 2)

Divide equation 1 by -5165:
{x+0 y = 2856/1115 | (equation 1)
{0 x+y = 2970987/223 | (equation 2)

Collect results:

Answer:  {x = 2856/1115 , y = 2970987/223

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Solve the following system using substitution:
{y = 4050 x + 2949
{y = 5165 x + 93

Substitute y = 4050 x + 2949 into the second equation:
{y = 4050 x + 2949
{4050 x + 2949 = 5165 x + 93


In the second equation, look to solve for x:
{y = 4050 x + 2949
{4050 x + 2949 = 5165 x + 93


Subtract 5165 x + 2949 from both sides:
{y = 4050 x + 2949
{-1115 x = -2856


Divide both sides by -1115:
{y = 4050 x + 2949
{x = 2856/1115


Substitute x = 2856/1115 into the first equation:
{y = 2970987/223
{x = 2856/1115

Collect results in alphabetical order:
Answer:  {x = 2856/1115, y = 2970987/223