To use the process of elimination, we can eliminate one variable by adding or subtracting the two given equations. By doing so, the eliminated variable will cancel out and we can solve for the remaining variable.
To begin, let's eliminate y. We can do this by adding the two given equations.
(-3x + y) + (7x + y) = 17 + (-23)
Combining like terms, we have:
4x + 2y = -6
Since we need to eliminate another variable, let's eliminate y again. We can do so by subtracting the original first equation from the new equation we just obtained.
(4x + 2y) - (-3x + y) = -6 - 17
Simplifying, we get:
4x + 2y + 3x - y = -23 - 17
7x + y = -40
Now, we have a system of two equations:
4x + 2y = -6
7x + y = -40
To eliminate y once more, we can multiply the second equation by -2 and then add it to the first equation.
-2(7x + y) + (4x + 2y) = -2(-40) + (-6)
Simplifying, we have:
-14x - 2y + 4x + 2y = 80 - 6
-10x = 74
x = -7.4
Substituting this value of x into one of the original equations, we can solve for y. Let's use the first equation:
-3x + y = 17
-3(-7.4) + y = 17
22.2 + y = 17
y = 17 - 22.2
y = -5.2
Therefore, the values of x and y that satisfy the given system of equations are:
x = -7.4
y = -5.2
Use the process of elimination
-3x+y=17
7x+y=-23
x=
y=
1 answer
1 answer