Question

Use addition or substitution to find the value of x for this set of equations.
y = x - 2
7y - 4x = 10

Answer 1

keep the top as is, however the bottom you want to move the 7y over to the right behind the equal sign and -4x becomes positive 4x and move it over to the left. put 10 in the spot -4x was. This would cause the negative to be a positive sign making 10 a positive. your problem should now look like this:

y=x-2
4x+10=7y




Now you will want to substitute your y varable in the second equation with the y variable in the first equation. Now your answer should look like this:


4x+10=7(x-2)
4x+10=7x-14
now subtract both sides by -7
-3x+10=-14 is what youy should get

now subtract -10 on both sides

now you get -3x=-24
divde by both sides
x=8
is your answer for x

now plug in 8 into the first equation where x is the variable and you get:

y=8-2
y=6
so now you have
y =6
as your answer for y
so your solutions are:
{(8,6)}

Answer 2

Substitution would be the best. You would want to "substitute the 1st equation into the second, and then rewrite it. So, it would look like this:
7(x-2)-4x=10
Next, use the distributive property:
7x-14-4x=10
Simply Simplify:
3x-14=10
Solve it (almost):
3x-14=10
+14 +14
Ok...
3x=24

Fianlly: X=8

So then after we find the X value, we plug this in to the Y= equation to get our Y value:

y=x-2
y=(8)-2
Y=6
X=8
coordinates:
[x,y]
[8,6]

Thank You. ~CHR