Question

The elimination method was used to solve the following system of equations:

x − 6y = 30
5x − 2y = −46

Which of the following is the correct y-coordinate of the solution?

−12
−7
7
12

Answer 1

-7

Explanation:

To solve this system of equations, let's solve for x first. We can move 6y to the other side of the first equation by adding it to both sides. Now we know what x equals:

x = 30 + 6y.

Now, we can substitute that equation in for every x in the 2nd equation, then solve for y.

The second equation becomes:

5(30+6y) - 2y = -46

(150 + 30y) - 2y = -46

Simplify.

150 + 28y = -46

Subtract 150 from both sides

28y = -196

Divide by 28 (to get y by itself)

y = -7

Answer 2

y = -7

Explanation:

Given system of equations:

`\begin{cases}x-6y = 30\\5x-2y =-46\end{cases}`

Multiply the first equation by -5:

`\implies -5(x-6y)=-5(30)`

`\implies -5x+30y=-150`

Add this to the second equation to eliminate the term in x:

`\begin{array}{crcrcl}& 5x & - & 2y & = & \:\:-46\\+&(-5x&+&30y&=&-150)\\\cline{2-6}&&&28y&=&-196\\ \cline{2-6}\end{array}`

Solve the equation for y:

`\implies 28y=-196`

`\implies (28y)/(28)=(-196)/(28)`

`\implies y=-7`