Question

Question 7: Solve this system

A.(15, 10)
B.(-15, 10)
C.(-10, 25)
D.(10, 15)

Answer 1

D. (10, 15)

Explanation:

Hi there!

We are given the following system:

`(1)/(2)x`+y=20

x+4y=70

And we want to solve it (find the values of x and y).

Let's use substitution for this problem, where we will isolate one variable on one side, while the other side contains an expression with the other variable. Then, we use the expression to solve for the variable that the expression contains, then use the value of that variable to solve for the aforementioned isolated variable.

Subtract
`(1)/(2)x` from both sides in the first equation

y=20-
`(1)/(2)x`

Now substitute 20-
`(1)/(2)x` as y in x+4y=70

x+4(20-
`(1)/(2)x`)=70

Do the distributive property

x+80-2x=70

Combine like terms on the left

-x+80=70

Subtract 80 from both sides

-x=-10

Multiply both sides by -1

x=10

We found the value of x. Now let's use that value to find what y is

Since we know that y=20-
`(1)/(2)x` and x=10, we can substitute 10 as the value of x to solve for y

In that case,

y=20-
`(1)/(2)`(10)

Multiply

y=20-5

Subtract

y=15

The answer is x=10, y=15, or as a point, (10, 15), aka D

Hope this helps!