Lesson 14
Solving More Systems
Let’s solve systems of equations.
Problem 1
Solve: \(\begin{cases} y=6x \\ 4x+y=7 \\ \end{cases}\)
Problem 2
Solve: \(\begin{cases} y=3x \\ x=\text-2y+70 \\ \end{cases}\)
Problem 3
Which equation, together with \(y=\text-1.5x+3\), makes a system with one solution?
A:
\(y=\text-1.5x+6\)
B:
\(y=\text-1.5x\)
C:
\(2y=\text-3x+6\)
D:
\(2y+3x=6\)
E:
\(y=\text-2x+3\)
Problem 4
The system \(x-6y=4\), \(3x-18y=4\) has no solution.
-
Change one constant or coefficient to make a new system with one solution.
-
Change one constant or coefficient to make a new system with an infinite number of solutions.
Problem 5
Match each graph to its equation.
![Four graphs, each with a line in the x y plane.](https://cms-im.s3.amazonaws.com/qaPUjm1sBjLj27HhQixvPd58?response-content-disposition=inline%3B%20filename%3D%228-8.3.C.PP.Image.03.7.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C.PP.Image.03.7.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T181818Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ab61d8b389a45d44113e416689683ecb3530052f8f75f3229023e9c57b287988)
- \(y=2x+3\)
- \(y=\text-2x+3\)
- \(y=2x-3\)
- \(y=\text-2x-3\)
Problem 6
Here are two points: \((\text-3,4)\), \((1,7)\). What is the slope of the line between them?
A:
\(\frac43\)
B:
\(\frac34\)
C:
\(\frac16\)
D:
(From Unit 3, Lesson 10.)
\(\frac23\)