Solve the following simultaneous equations:
$$x + y = 2$$
$$x - 3y = -2$$ - Edexcel - GCSE Maths - Question 12 - 2022 - Paper 1
Question 12
Solve the following simultaneous equations:
$$x + y = 2$$
$$x - 3y = -2$$
Worked Solution & Example Answer:Solve the following simultaneous equations:
$$x + y = 2$$
$$x - 3y = -2$$ - Edexcel - GCSE Maths - Question 12 - 2022 - Paper 1
Step 1
For a correct method to eliminate either variable or rearrangement of one equation leading to substitution (condone one arithmetic error)
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Answer
To solve the simultaneous equations, we can first rearrange one of the equations to isolate a variable. Let's take the first equation:
x+y=2
We can rearrange it to get:
x=2−y
Now we can substitute this expression for x into the second equation.
Step 2
For either correct value of x or correct value of y
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Answer
Now, substitute x=2−y into the second equation:
x−3y=−2(2−y)−3y=−2
Combining like terms, we have:
2−4y=−2
Subtracting 2 from both sides gives:
−4y=−4
Dividing by -4 yields:
y=1
Now, substituting y=1 back into x+y=2:
x+1=2
Thus, we find:
x=1.
Step 3
(a) For a correct substitution of found values into one of the equations as a correct method leading to the second values (condone one arithmetic error)
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Answer
Finally, substituting x=1 and y=1 back into the original equations to verify:
For the first equation:
x+y=21+1=2 (True)
For the second equation:
x−3y=−21−3(1)=−21−3=−2 (True)
Both equations are satisfied, confirming that the solution is correct.
