# Common Core: High School - Algebra : Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

## Example Questions

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### Example Question #1 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case,  ,  ,  .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #2 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case,  , ,  .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #3 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case,  ,  ,  .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #4 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case, , , .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #5 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case, .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #6 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case, .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #7 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

4

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case, .

Now plug these values in.

Split this up into  equations.

b

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #8 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and  . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case, .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #9 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and. Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case, .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

### Example Question #10 : Solve Simple System Of Two Variable Linear And Quadratic Equations: Ccss.Math.Content.Hsa Rei.C.7

Find the points of intersection of  and . Round your answers to the nearest hundredth.

Explanation:

The first step to solving this problem is to set the equations equal to each other.

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

Where , , and  correspond to coefficients in the following quadratic equation.

In this case, .

Now plug these values in.

Split this up into  equations.

Since we want points, we need to plug these values into one of the original equations.

So the first intersection point is at

Now we need to find the last point of intersection.

So the second intersection point is at

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