Answer:
C. (1,4)
Explanation:
Hi there!
We are given the following system of equations:
5x + y = 9
10x - 7y = -18
And we want to solve it.
Let's use elimination for this system, where we will add the two equations together to clear one of the variables, solve for the other variable, and then use the value of the solved variable to find the value of the variable we originally cleared
Since we are clearing a variable, we want the coefficients in front of the variables to have opposite signs; for example, 3 and -3.
Before we add the equations together, we can multiply or divide an equation by a specific number.
Let's clear out the y's. The coefficient in front of y in the first equation is 1, while in the second, it's -7
Let's multiply both sides by 7 in the first equation.
7(5x + y)=9*7
35x + 7y = 63
Now stack it up with the other equation:
35x + 7y = 63
10x - 7y = -18
Add the equations together
45x=45
Divide both sides by 45
x=1
Now substitute 1 as x into either one of the equations to solve for y
Taking 10x-7y=-18 for instance,
10(1)-7y=-18
Multiply
10-7y=-18
Subtract 10 from both sides
-7y=-28
Divide both sides by -7
y=4
The answer is x=1, y=4, or as a point, (1,4) which is also C.
Hope this helps!