Use the graph to solve the system of linear equations. Check your solution

Question

y = 1/2x - 1

y= 4x + 6

Answer 1

y = 1/2x – 1

y = 4x + 6

You can solve a system of equations by graphing, elimination, substitution, or a combination of these methods.

Since each of these equations are in slope-intercept form, I would simply set them equal to each other; they each define y in a different way, but we can set the two y's equal to each other, since y is y.

1/2 x — 1 = 4x + 6

I'm going to multiply through by two to get rid of the fraction. You'll see that I simply doubled each term in the equation.

1x – 2 = 8x + 12

Now I will put the x's on one side of the equation and the integers on the other, by adding and subtracting.

1x – 2 = 8x + 12

–1x –12 –1x –12

–14 = 7x

Now I need to divide by 7 on each side so that I know what 1x equals.

–14 = 7x

___ ____

7 7

x = –2

We know what x is. We need to determine the value of y when x is –2. We can substitute this value of x in either of the two original equations.

y = 1/2x – 1 <one of original equations>

y = (1/2)(–2) – 1

y = (–2/2) – 1

y = (–1) – 1

y = –2

The two lines defined by the two original equations intersect at the point (–2 , –2). You were asked to check these values for x and y in the two original equations.

–2 =?= (1/2)(–2) – 1

–2 =?= (–2/2) – 1

– =?= –1 – 1

–2 = –2 One check confirmed. Now we need to check the second original equation.

–2 =?= (4)(–2) + 6

–2 =?= –8 + 6

–2 = –2 Second check confirmed. Point (–2 , –2) is on each line. It is the intersection point.

Answer 2

Hi Ashlyn U.

 

y = 1/2x - 1

y= 4x + 6

You can graph both your equations at Desmos.com (Graphing Calculator) on the same grid to see the coordinates of their intersection, then plug those values into your equations to check them.

You can also graph them on paper quickly as follows

For each line obtain the x and y intercepts this will give two points for each line

y = 1/2x - 1

(0, -1) (2, 0)

For the next line

y= 4x + 6

(0, 6) (-3/2, 0)

Give it a try.