Question

2. A system of equations is given below.
2x + 7y = 1
-3x – 4y = 5
a. Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.
b. Use any method to solve the equivalent system of equations (the new first equation with the original second equation).
c. Prove that the solution for the equivalent system is the same as the solution for the original system of equations.

Answer 1

@chaser71

Answer 2

a) Let's multiply this equation by 2:
\(2(2x+7y)=2(1)\)
becomes:
\(4x+14y=2\)

Add it to the 2nd equation:
\(4x-3x+(14y-4y)=2+5\)
\(x+10y=7\)

b) Let's solve for \(x\):
\(x=7-10y\)

Now replace \(x\) into the 1st equation:
\(4(7-10y)+14y=2\)
\(28-40y+14y=2\)
\(-26y=2-28\)
\(-26y=-26\)
\(y=1\)

Now you have the value for \(y\), so you can plug it into the second equation:
\(x+10(1)=7\)
\(x=7-10\)
\(x=-3\)

Answer 3

woaw tanks very much buddy!

Answer 4

np

It is very similar to do it for c)... just solve for x in one equation, then plug this into the 2nd equation... and then you can find the value of y. Then with this, you can plug y into any equation to find the value of x

Answer 5

aight thank u brah

Answer 6

yw!