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

User Ktsangop
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1 Answer

9 votes

Answer:

x = 2 and y =16

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

User Guymage
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3.7k points