Question

An unknown number y is 10 more than an unknown number x. The number y is also x less than 3. The equations to find x and y are shown below. y = x + 10 y = −x + 3 Which of the following statements is a correct step to find x and y? Add the equations to eliminate x. Multiply the equations to eliminate y. Write the points where the graphs of the equations intersect the x-axis. Write the points where the graphs of the equations intersect the y-axis.

Answer 1

(0,3) and (0,10) are the y- intercepts
(-3.5, 6.5) is the point of interception
Add the equations to eliminate x

Answer 2

The correct option is A.

Explanation:

Let two unknown numbers are x and y.

An unknown number y is 10 more than an unknown number x.

`y=10+x` ... (1)

The number y is also x less than 3.

`y=-x+3` .... (2)

We can use elimination method to solve the system of inequality.

In equation (1) and (2), the coefficient of x is same with opposite sign.

Add the equations to eliminate x.

`y+y=x+10-x+3`

`2y=13`

Divide both sides by 2.

`y=6.5`

Substitute y=6.5 in equation (1).

`6.5=10+x`

`6.5-10=x`

`-3.5=x`

The value of xis -3.5 and value of y is 6.5.

Therefore the correct option is A.