Explore: Write down the system in your homework and solve the system by hand. Check your answer by dragging the red "solution" dot to the point of intersection Assume the graph has a scale of [1:1]. If you want more practice, click on the "New Points" button.
Solve the system of linear equations by graphing.
1)\( \begin{align*} & y=2x+4\\ & y=-x+10\\ \end{align*} \)
2) \( \begin{align*} & y=-\dfrac{1}{2}x+4 \\ & y=-x\\ \end{align*} \)
3) \( \begin{align*} & y=2x+3 \\ & y-x=-3\\ \end{align*} \)
4) \( \begin{align*} & y=x-6\\ & y=\dfrac{1}{3}x-4 \\ \end{align*} \)
5) \( \begin{align*} & y=-\dfrac{1}{2}x+1\\ & y=\dfrac{3}{5}x-10\\ \end{align*} \)
6) \( \begin{align*} & y-3=-\dfrac{1}{2}(x+1)\\ & y+7=2(x+1)\\ \end{align*} \)
7) \( \begin{align*} & y+1=\dfrac{2}{3}(x-1)\\ & y-2=-\dfrac{3}{2}(x+1)\\ \end{align*} \)
Solve the system of linear equations by using substitution.
8) \( \begin{align*} & -7x+2y=7\\ & y=6x+1\\ \end{align*} \)
9) \( \begin{align*} & 2x+9y=-4\\ & x-2y=11\\ \end{align*} \)
10) \( \begin{align*} & -5x-y=12\\ & 3x-5y=4\\ \end{align*} \)
11) \( \begin{align*} & y=-x+3\\ & 3x-5y=25\\ \end{align*} \)
12) \( \begin{align*} & x+y=11\\ & 60x+55y=635\\ \end{align*} \)
13) \( \begin{align*} & y+2=\dfrac{1}{4}(x+1)\\ & y-3=-4(x-2)\\ \end{align*} \)
14) \( \begin{align*} & y+1=\dfrac{1}{2}(x+2)\\ & y-1=2(x-2)\\ \end{align*} \)
Solve the system of linear equations by using elimination.
15) \( \begin{align*} & x+5y=28\\ & -x-2y=-13\\ \end{align*} \)
16) \( \begin{align*} & 6x+y=39\\ & -2x+y=-17\\ \end{align*} \)
17) \( \begin{align*} & 2y-3x=10\\ & 7x=-2y-50\\ \end{align*} \)
18) \( \begin{align*} & 6x+5y=19\\ & 2x+3y=5\\ \end{align*} \)
19) \( \begin{align*} & 4x+5y=35\\ & 2y=3x-9\\ \end{align*} \)
20) \( \begin{align*} & y+1=3x+6\\ & -y+1=2x+1\\ \end{align*} \)
21) \( \begin{align*} & 2y-5=x+3\\ & 4y+1=3x-2\\ \end{align*} \)
15) \( \begin{align*} & x+5y=28\\ & -x-2y=-13\\ \end{align*} \)
16) \( \begin{align*} & 6x+y=39\\ & -2x+y=-17\\ \end{align*} \)
17) \( \begin{align*} & 2y-3x=10\\ & 7x=-2y-50\\ \end{align*} \)
18) \( \begin{align*} & 6x+5y=19\\ & 2x+3y=5\\ \end{align*} \)
19) \( \begin{align*} & 4x+5y=35\\ & 2y=3x-9\\ \end{align*} \)
20) \( \begin{align*} & y+1=3x+6\\ & -y+1=2x+1\\ \end{align*} \)
21) \( \begin{align*} & 2y-5=x+3\\ & 4y+1=3x-2\\ \end{align*} \)
Determine which method would be most efficient to use to solve each system. Then, solve the system using that method.
22) \( \begin{align*} & y=x+4\\ & y=-3x-2\\ \end{align*} \)
23) \( \begin{align*} & 5x+y=-4\\ & x-y=-2\\ \end{align*} \)
24) \( \begin{align*} & -0.45x-y=1.35\\ & -1.8x+y=-1.8\\ \end{align*} \)
25) \( \begin{align*} & 3x-2y=-5\\ & 4x+3y=-18\\ \end{align*} \)
26) \( \begin{align*} & y=3x+12\\ & y=-4x-2\\ \end{align*} \)
27) \( \begin{align*} & \dfrac{1}{2}x+\dfrac{3}{4}y=5\\ & x-12y=6\\ \end{align*} \)
28) \( \begin{align*} & -7x+2y=7\\ & y=6x+1\\ \end{align*} \)
29) \( \begin{align*} & y=3x+2\\ & x=11-2y\\ \end{align*} \)
30) \( \begin{align*} & x-2y=-6\\ & 4x+6y=4\\ \end{align*} \)
31) \( \begin{align*} & 4x-5y=35\\ & 2y=3x-9\\ \end{align*} \)
22) \( \begin{align*} & y=x+4\\ & y=-3x-2\\ \end{align*} \)
23) \( \begin{align*} & 5x+y=-4\\ & x-y=-2\\ \end{align*} \)
24) \( \begin{align*} & -0.45x-y=1.35\\ & -1.8x+y=-1.8\\ \end{align*} \)
25) \( \begin{align*} & 3x-2y=-5\\ & 4x+3y=-18\\ \end{align*} \)
26) \( \begin{align*} & y=3x+12\\ & y=-4x-2\\ \end{align*} \)
27) \( \begin{align*} & \dfrac{1}{2}x+\dfrac{3}{4}y=5\\ & x-12y=6\\ \end{align*} \)
28) \( \begin{align*} & -7x+2y=7\\ & y=6x+1\\ \end{align*} \)
29) \( \begin{align*} & y=3x+2\\ & x=11-2y\\ \end{align*} \)
30) \( \begin{align*} & x-2y=-6\\ & 4x+6y=4\\ \end{align*} \)
31) \( \begin{align*} & 4x-5y=35\\ & 2y=3x-9\\ \end{align*} \)
Review
32) Solve the equation for \(y\): \(-3x - 7y = 21\)
33) Solve the equation for \(y\): \(8x + 5y = -20\)
34) Solve the equation for \(y\): \(2x - 9y = 18\)