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Solutions
48 Videos

Solve each system by graphing. Check your solutions.

```
\displaystyle
y=x-5\\y=3-x
```

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Q1a

Solve each system by graphing. Check your solutions.

```
\displaystyle
m+2 n=2\\3 m+2 n=-6
```

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Q1b

Solve each system by graphing. Check your solutions.

```
\displaystyle
p-q=1\\p+2 q=7
```

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Q1c

Solve each system by graphing. Check your solutions.

```
\displaystyle
2 x+y=2\\2 x+y+4=0
```

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Q1d

Solve each system by graphing. Check your solutions.

```
\displaystyle
x-y-4=0\\5 x-y-8=0
```

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Q1e

Solve each system by graphing. Check your solutions.

```
\displaystyle
a+b=4\\3 a=12-3 b
```

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Q1f

Solve each system by graphing. Check your solutions.

```
\displaystyle
3 x-2 y=-8\\x-2 y=-4
```

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Q1g

Solve each system by graphing. Check your solutions.

```
\displaystyle
2 x-y=-4\\2 x+y=6
```

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Q1h

Solve each system graphically.

```
\displaystyle
4 x+3 y=1\\4 x-3 y=14
```

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Q2a

Solve each system graphically.

```
\displaystyle
3 x+y=1\\x+4 y=3
```

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Q2b

Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.

```
\displaystyle
\begin{aligned} & 3 c+d=4 \\ & 6 c+2 d=8 \end{aligned}
```

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Q3a

Without graphing, determine whether each system has one solution no solution, or infinitely many solutions.

```
\displaystyle
4 x-2 y=0\\2 x-y=3
```

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Q3b

Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.

```
\displaystyle
x+5 y=9\\x-y=3
```

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Q3c

Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.

```
\displaystyle
x+2 y-7=0\\3 x+6 y-14=0
```

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Q3d

The two largest deserts in the world are the Sahara Desert and the Australian Desert. The sum of their areas is 13 million square kilometres. The area of the Sahara Desert is 5 million square kilometres more than the area of the Australian Desert. Solve the following system graphically to find the area of each desert, in millions of square kilometres.

```
\displaystyle
s+a=13\\s=a+5
```

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Q4

Profit A company manufactures and sells paddles. Its manufacturing
costs are ` \$ 500 `

, plus ` \$ 10 `

per paddle. The company sells the paddles for ` \$ 18 `

.
The cost and revenue can be represented by the following system of equations.

Dollar Cost: ` \quad d=500+10 p `

Dollar Revenue: ```
\displaystyle
d=18 p
```

a) What does each variable represent?

b) Solve the system graphically.

c) How many paddles must be sold for the company to make a profit?

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Q5

Solve each system by substitution. Check each solution.

```
\displaystyle
y=6-2 x\\3 x+2 y=10
```

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Q6a

Solve each system by substitution. Check each solution.

```
\displaystyle
3 x+y-2=0\\5 x+2 y-3=0
```

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Q6b

Solve each system by substitution. Check each solution.

```
\displaystyle
3 s+5 t=2\\s+4 t=-4
```

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Q6c

Solve each system by substitution. Check each solution.

```
\displaystyle
x+4 y=-3\\2 x+8 y=-6
```

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Q6d

Solve each system by substitution. Check each solution.

```
\displaystyle
3 x+2 y=9\\-x+3 y=8
```

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Q6e

Solve each system by substitution. Check each solution.

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Q6f

Solve each system by substitution. Check each solution.

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Q6g

Solve each system by substitution. Check each solution.

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Q6h

Simplify each system, and then solve it by substitution. Check each solution.

```
\displaystyle
2(x-1)+y=2\\3 x-4(y+3)=5
```

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Q7a

Simplify each system, and then solve it by substitution. Check each solution.

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Q7b

Which method would you use to solve each system of equations? Explain. Then, solve and check each system.

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Q10a

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Q10b

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Q10c

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Q10d