Question

Solve Each System by Elimination:-3x+4y=-8-3x+2y=-10

Answer 1

Answer : x = 4 and y = 1

We are given the below system of equations

-3x + 4y = -8

-3x + 2y = -10

This system of equations can be solve using elimination method

To use elimination method, we need to eliminate one of the variables

-3x + 4y = -8 -------------- equation 1

-3x + 2y = -10 ------------- equation 2

Since, the coefficient of x is the same in both equations, then, we can eliminate the variable x

To eliminate x, substract equation 2 from 1

-3x - (-3x) + 4y - 2y = -8 - (-10)

minus x minus = plus; According to the basic rule of mathematics

-3x + 3x + 4y - 2y = -8 + 10

0 + 2y = 2

2y = 2

Divide both sides by 2

`\begin{gathered} (2y)/(2)\text{ = }(2)/(2) \\ y\text{ = 1} \end{gathered}`

To find x, substitute the value of y = 1 into equation 1

-3x + 4y = -8

-3x + 4(1) = -8

-3x + 4 = -8

Isolate -3x

-3x = -8 - 4

-3x = - 12

Divide both sides by -3

`\begin{gathered} (-3x)/(-3)\text{ = }(-12)/(-3) \\ x\text{ = }(12)/(3) \\ x\text{ = 4} \end{gathered}`

Hence, x = 4 and y = 1: (4, 1)