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Solve the system of equations −2x+y=12 and 7x-7y=-49x by combining the equations.

Sagot :

Semsee45idn

Answer:

x = 2 and y =16

Step-by-step explanation:

Method 1

Rewrite  -2x + y = 12  to make y the subject:

Add 2x to both sides:   y = 12 + 2x

Now substitute  y = 12 + 2x   into   7x - 7y = -49x and solve for x:

                                             7x - 7(12 + 2x) = -49x

Multiply out the brackets:     7x - 84 - 14x = -49x

Collect like terms:                 7x - 14x - 84 = -49x

Combine like terms:                     -7x - 84 = -49x

Add 7x to both sides:                          -84 = -42x

Divide both sides by -42:                         2 = x

Therefore, x = 2

Now we have found the value of x, substitute this into  y = 12 + 2x  to find y:

y = 12 + (2 x 2)

 = 12 + 4

 = 16

Therefore, x = 2 and y =16

Method 2

Rewrite  -2x + y = 12  to make y the subject:

Add 2x to both sides:   y = 12 + 2x

Rewrite  7x - 7y = -49x  to make y the subject:

Subtract 7x from both sides:   -7y = -56x

Divide both sides by -7:              y = 8x

Equate both equations and solve for x:

                                                            y = y

                                                   12 + 2x = 8x

Subtract 2x from both sides:             12 = 6x  

Divide both sides by 6:                       2 = x

Therefore, x = 2

Now substitute x = 2 into any of the two equations to find y:

y = 8x

y = 8 x 2

y = 16

Therefore, x = 2 and y = 16

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