Question

I need help solve each system by the equal method.

Answer 1

The solution (x, y) = (3, -2)

Step-by-step explanation:

y = -x + 1

y = 2/3x - 4

Using the equal method:

we would equate both equation together. This because they are both equal to y

y = y

-x + 1 = 2/3x - 4

`\begin{gathered} -x+1=(2)/(3)x-4 \\ \text{add x to both sides:} \\ -x\text{ + x }+1=(2)/(3)x+x-4 \\ \end{gathered}`
`\begin{gathered} 0+1=(2x+3(x))/(3)-4 \\ 1\text{ = }(5x)/(3)-4 \\ \text{add 4 to both sides:} \\ 1+4\text{ = }(5x)/(3)-4+4 \end{gathered}`
`\begin{gathered} 5\text{ = }(5x)/(3)+0 \\ (5)/(1)\text{ = }(5x)/(3) \\ cross\text{ multiply}\colon \\ 5(3)\text{ = 5x} \\ 15\text{ = 5x} \\ \text{divide both sides by 5:} \\ \frac{15}{5\text{ }}=\text{ }\frac{\text{5x}}{5} \\ 3\text{ = x} \end{gathered}`

We replace x in any of the equation with 3 to get y:

using the first equation: y = -x + 1

y = -3 + 1

y = -2

The solution or the point of intersection (x, y) = (3, -2)