Question

Trevor solved the equations . . .

Answer 1

Trevor solved the system of equations below. What mistake did he make in his work?

2x + y = 5
x − 2y = 10

y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 0
x = 0

2(0) + y = 5
y = 5

He should have substituted 5 + 2x
He combined like terms incorrectly, it should have been 4x instead of 5x
He subtracted 10 from the right side instead of adding 10 to the right side
He made no mistake

Answer 2

if you rearrange the first equation in the form y=ax+b
so you have
2x+y=5
rearrange to get y+2x=5
then we have y+2x, we want y on its own so we must make +2x become 0
to get from 2x to 0, we subtract 2x
this is the opposite action to addition

+ -
x /
so opposite to + is -, opposite to - is +
opposite to x is / and opposite to / is x (where x is multiply)

so we have

y+2x=5
y+2x-2x=5-2x
y+0=5-2x
y=5-2x

so now we know what y is equal to, so for example if i had

a+3=5
and I knew that a was 2, I would just let a=2, so I got 2+3=5

so in your question we know that y=5-2x

so we have
x − 2y = 10
so we let y=5-2x

x-2(5-2x)=10

x-10+4x=10
x+4x=20
5x=20
x=20/5

hence x=4

so letting x=4, we substitute into the first equation to get

2x + y = 5
2(4)+y=5
8+y=5
y=-3

so x=4, y=-3

the part that differs to the parts given in the question is

x-10+4x=10
x+4x=20


we have x+4x=20, they have x+4x=0

so we look at the step
x-10+4x=10

this step wants us to rearrange for x, so to do that we have

5x-10=10
we must make -10 become 0, to get from -10 to 0 we must +10
so
5x-10+10=10+10
5x-0=20
5x=20

the person in the question had

x+4x=0
5x=0

this means he must have subtracted 10 instead of adding10

hence his mistake is He subtracted 10 from the right side instead of adding 10 to the right side

Answer 3

thanks