What are the solutions to the system y=x^2+5x-9 y=2x+1
2 answers:
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<u>ANSWER: </u>
The solution of the two equations 2x+3y=5 and 4x - y=17 is (4, -1).
<u>SOLUTION: </u>
Given, two linear equations are 2x + 3y = 5 → (1) and 4x – y = 17 → (2).
Let us first solve the above equations using <em>elimination process. </em>
For elimination, one of the coefficients of variables has to be same in order to cancel them.
Now solve (1) and (2)
eqn (1) 2 → 4x + 6y = 10
eqn (2) → 4x – y = 17
(-) ----------------------------
0x + 7y = -7
y = -1
Substitute y value in (2)
So, solution of two equations is (4, -1).
<u><em>Now let us solve using substitution process.</em></u>
Then, (2) → 4x – y = 17 → 4x = 17 + y → y = 4x – 17
Now substitute y value in (1) → 2x + 3(4x – 17) = 5 → 2x + 12x – 51 = 5 → 14x = 5 + 51 → 14x = 56
x = 4
Substitute x value in (2) → y = 4(4) – 17 → y = 16 – 17 → y = -1
Hence, the solution of the two equations is (4, -1).
Answer:
The measure of the angles are
m∠1=128°
m∠2=52°
m∠3=52°
m∠4=128°
m∠5=128°
m∠6=128°
m∠7=52°
m∠8=52°
Step-by-step explanation:
see the attached figure with numbers to better understand the problem
step 1
Find the measure of angle 5
we know that
m∠5+52°=180° ----> by consecutive interior angles
m∠5=180°-52°=128°
step 2
Find the measure of angle 8
we know that
m∠8=52° ----> by vertical angles
step 3
Find the measure of angle 7
we know that
m∠7=m∠8 ----> by corresponding angles
we have
m∠8=52°
therefore
m∠7=52°
step 4
Find the measure of angle 6
we know that
m∠6+m∠7=180° ----> by supplementary angles
we have
m∠7=52°
therefore
m∠6+52°=180°
m∠6=180°-52°=128°
step 5
Find the measure of angle 3
we know that
m∠3+m∠6=180° ----> by consecutive interior angles
we have
m∠6=128°
m∠3=180°-128°=52°
step 6
Find the measure of angle 2
we know that
m∠2=m∠3 ----> by vertical angles
we have
m∠3=52°
therefore
m∠2=52°
step 7
Find the measure of angle 1
we know that
m∠1+m∠3=180° ----> by supplementary angles
we have
m∠3=52°
therefore
m∠1+52°=180°
m∠1=180°-52°=128°
step 8
Find the measure of angle 4
we know that
m∠4=m∠1 ----> by vertical angles
we have
m∠1=128°
therefore
m∠4=128°
