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
